%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP209-1 : 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 : n010.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 10:13:20 AM UTC 2026
% Result : Unsatisfiable 2.21s 2.01s
% Output : Refutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 43
% Syntax : Number of formulae : 264 ( 18 unt; 19 def)
% Number of atoms : 781 ( 272 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1004 ( 487 ~; 498 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 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 : 61 ( 0 sgn 61 !; 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_c1,sk_c2) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f67]) ).
fof(f75,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f81]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c10,X2) != sk_c9
| multiply(X3,sk_c10) != X2
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c9
| multiply(X6,X7) != sk_c9
| inverse(X6) != X7
| multiply(X7,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| sk_c10 != multiply(X1,sk_c9)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
fof(f92,plain,
! [X3,X0,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f91]) ).
fof(f93,plain,
! [X3,X0,X6,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) ),
inference(equality_resolution,[],[f92]) ).
fof(f95,definition,
( spl0_1
<=> ! [X6] :
( sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f96,plain,
( ! [X6] :
( sk_c9 != multiply(inverse(X6),sk_c10)
| sk_c9 != multiply(X6,inverse(X6)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_2
<=> ! [X5] :
( sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f99,plain,
( ! [X5] :
( sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_3
<=> ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f102,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,definition,
( spl0_4
<=> ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f105,plain,
( ! [X3] :
( sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10)) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl0_5
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f93,f107,f104,f101,f98,f95]) ).
fof(f115,definition,
( spl0_7
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f117,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f130,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = inverse(sk_c6)
| ~ 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_c10 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f137,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| ~ 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_c10 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f142,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| ~ 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_c10 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f147,plain,
( sk_c10 = inverse(sk_c5)
| ~ 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_c4 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f152,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f156,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f150,f130]) ).
fof(f157,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f150,f135]) ).
fof(f158,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f150,f140]) ).
fof(f159,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f150,f145]) ).
fof(f161,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c10,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f163,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ 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(f169,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f50,f161,f140]) ).
fof(f170,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f161,f145]) ).
fof(f183,definition,
( spl0_17
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f185,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f183]) ).
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,definition,
( spl0_18
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f196,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f200,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f194,f130]) ).
fof(f201,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f194,f135]) ).
fof(f202,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f194,f140]) ).
fof(f203,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f194,f145]) ).
fof(f205,plain,
( sk_c10 != sk_c10
| sk_c9 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f99,f137]) ).
fof(f206,plain,
( sk_c9 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f205]) ).
fof(f211,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f206,f135,f98,f130]) ).
fof(f214,plain,
( sk_c10 != sk_c9
| sk_c9 != inverse(identity)
| ~ spl0_2 ),
inference(superposition,[],[f99,f1]) ).
fof(f215,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f185]) ).
fof(f218,plain,
( identity = multiply(sk_c10,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f117]) ).
fof(f225,definition,
( spl0_20
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f226,plain,
( identity = sk_c10
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f227,plain,
( identity != sk_c10
| spl0_20 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f232,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c10,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f196]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f231,f1]) ).
fof(f244,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f215]) ).
fof(f245,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f244,f1]) ).
fof(f257,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f245,f196]) ).
fof(f266,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f232,f257]) ).
fof(f268,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f266,f196]) ).
fof(f284,definition,
( spl0_21
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f286,plain,
( sk_c9 != inverse(identity)
| spl0_21 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f288,definition,
( spl0_22
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f289,plain,
( sk_c10 = sk_c9
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f291,plain,
( ~ spl0_21
| ~ spl0_22
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f214,f98,f288,f284]) ).
fof(f397,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f241,f268]) ).
fof(f402,plain,
( sk_c9 = multiply(inverse(sk_c6),sk_c10)
| ~ spl0_11 ),
inference(superposition,[],[f241,f137]) ).
fof(f411,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f241,f152]) ).
fof(f418,plain,
( sk_c10 = multiply(sk_c10,sk_c4)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f411,f117]) ).
fof(f422,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f397,f3]) ).
fof(f430,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f422,f194,f183,f225]) ).
fof(f431,plain,
( sk_c9 != inverse(sk_c10)
| ~ spl0_20
| spl0_21 ),
inference(superposition,[],[f286,f226]) ).
fof(f432,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_20 ),
inference(superposition,[],[f1,f226]) ).
fof(f466,plain,
( sk_c10 = sk_c9
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f163,f418]) ).
fof(f498,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f218,f432]) ).
fof(f506,plain,
( sk_c10 = sk_c3
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f498,f226]) ).
fof(f523,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f117,f506]) ).
fof(f539,plain,
( sk_c10 != sk_c9
| ~ spl0_7
| ~ spl0_20
| spl0_21 ),
inference(superposition,[],[f431,f523]) ).
fof(f549,plain,
( spl0_22
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f466,f161,f150,f115,f288]) ).
fof(f557,plain,
( ~ spl0_22
| ~ spl0_7
| ~ spl0_20
| spl0_21 ),
inference(avatar_split_clause,[],[f539,f284,f225,f115,f288]) ).
fof(f589,plain,
( sk_c10 = multiply(sk_c5,sk_c10)
| ~ spl0_12
| ~ spl0_22 ),
inference(forward_demodulation,[],[f142,f289]) ).
fof(f595,plain,
( sk_c9 = multiply(inverse(sk_c5),sk_c10)
| ~ spl0_12 ),
inference(superposition,[],[f241,f142]) ).
fof(f596,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c5,multiply(sk_c9,X0))
| ~ spl0_12 ),
inference(superposition,[],[f4,f142]) ).
fof(f597,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f595,f147]) ).
fof(f610,plain,
( sk_c9 != multiply(sk_c9,sk_c10)
| sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_1
| ~ spl0_10 ),
inference(superposition,[],[f96,f132]) ).
fof(f612,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f96,f117]) ).
fof(f623,definition,
( spl0_27
<=> sk_c9 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
fof(f624,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f641,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c10,multiply(sk_c5,sk_c10))
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f105,f147]) ).
fof(f644,plain,
( sk_c10 != sk_c10
| sk_c9 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f105,f117]) ).
fof(f645,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c3,sk_c10))
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f644]) ).
fof(f646,plain,
( sk_c9 != multiply(sk_c10,multiply(sk_c5,sk_c10))
| ~ spl0_4
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f641]) ).
fof(f647,plain,
( sk_c9 != multiply(sk_c10,sk_c4)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f645,f152]) ).
fof(f648,plain,
( sk_c10 != sk_c9
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f647,f418]) ).
fof(f689,plain,
( spl0_27
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f597,f145,f140,f623]) ).
fof(f825,plain,
( sk_c9 = multiply(sk_c9,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f402,f132]) ).
fof(f861,plain,
( multiply(sk_c5,sk_c9) = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f596,f825]) ).
fof(f864,plain,
( sk_c10 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f241,f825]) ).
fof(f866,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f864,f3]) ).
fof(f869,plain,
( sk_c9 = multiply(sk_c5,sk_c9)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(forward_demodulation,[],[f861,f624]) ).
fof(f870,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(forward_subsumption_resolution,[],[f866,f227]) ).
fof(f871,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(avatar_contradiction_clause,[],[f870]) ).
fof(f874,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(forward_demodulation,[],[f869,f142]) ).
fof(f895,plain,
( spl0_22
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f874,f623,f140,f135,f130,f288]) ).
fof(f930,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f646,f589]) ).
fof(f934,plain,
( $false
| ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f930,f624]) ).
fof(f935,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f934]) ).
fof(f938,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c10) )
| ~ spl0_3
| ~ spl0_22 ),
inference(forward_demodulation,[],[f102,f289]) ).
fof(f944,plain,
( identity = multiply(sk_c10,sk_c10)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f218,f506]) ).
fof(f953,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c5,sk_c10)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f938,f147]) ).
fof(f957,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f938,f117]) ).
fof(f958,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f957]) ).
fof(f959,plain,
( sk_c10 != multiply(sk_c5,sk_c10)
| ~ spl0_3
| ~ spl0_13
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f953]) ).
fof(f960,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f958,f506]) ).
fof(f964,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f959,f589]) ).
fof(f965,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f964]) ).
fof(f978,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),sk_c10)
| sk_c10 != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[],[f108,f289]) ).
fof(f986,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f978,f147]) ).
fof(f990,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_22 ),
inference(superposition,[],[f978,f117]) ).
fof(f999,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f986,f589]) ).
fof(f1004,plain,
( sk_c10 != sk_c9
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(forward_demodulation,[],[f999,f624]) ).
fof(f1010,plain,
( $false
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f1004,f289]) ).
fof(f1011,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f1010]) ).
fof(f1026,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f648,f289]) ).
fof(f1027,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1026]) ).
fof(f1136,plain,
( sk_c9 != multiply(sk_c6,sk_c9)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f610,f825]) ).
fof(f1138,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_22 ),
inference(forward_demodulation,[],[f612,f289]) ).
fof(f1152,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f1136,f137]) ).
fof(f1154,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1138,f506]) ).
fof(f1160,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f1152,f289]) ).
fof(f1161,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f1160]) ).
fof(f1162,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f1154,f289]) ).
fof(f1163,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f1162]) ).
fof(f1169,definition,
( spl0_32
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1174,plain,
( ~ spl0_32
| ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1163,f288,f225,f115,f95,f1169]) ).
fof(f1184,plain,
( ~ spl0_32
| ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f960,f288,f225,f115,f101,f1169]) ).
fof(f1192,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(forward_demodulation,[],[f990,f506]) ).
fof(f1193,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(duplicate_literal_removal,[],[f1192]) ).
fof(f1198,plain,
( ~ spl0_32
| ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f1193,f288,f225,f115,f107,f1169]) ).
fof(f1213,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f944,f226]) ).
fof(f1217,plain,
( spl0_32
| ~ spl0_7
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f1213,f225,f115,f1169]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f109]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f133]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f138]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f143]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s12,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s13,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s14,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f158]) ).
cnf(s15,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f159]) ).
cnf(s19,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f167]) ).
cnf(s20,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s21,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s22,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f170]) ).
cnf(s33,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s34,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s35,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s36,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f192]) ).
cnf(s40,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s41,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s42,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f202]) ).
cnf(s43,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f203]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f211]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f291]) ).
cnf(s53,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f430]) ).
cnf(s61,plain,
( ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| spl0_22 ),
inference(sat_conversion,[],[f549]) ).
cnf(s66,plain,
( ~ spl0_7
| ~ spl0_20
| spl0_21
| ~ spl0_22 ),
inference(sat_conversion,[],[f557]) ).
cnf(s79,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_27 ),
inference(sat_conversion,[],[f689]) ).
cnf(s82,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f871]) ).
cnf(s92,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_22
| ~ spl0_27 ),
inference(sat_conversion,[],[f895]) ).
cnf(s99,plain,
( ~ spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(sat_conversion,[],[f935]) ).
cnf(s102,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22 ),
inference(sat_conversion,[],[f965]) ).
cnf(s109,plain,
( ~ spl0_5
| ~ spl0_12
| ~ spl0_13
| ~ spl0_22
| ~ spl0_27 ),
inference(sat_conversion,[],[f1011]) ).
cnf(s113,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_22 ),
inference(sat_conversion,[],[f1027]) ).
cnf(s130,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_22 ),
inference(sat_conversion,[],[f1161]) ).
cnf(s133,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22
| ~ spl0_32 ),
inference(sat_conversion,[],[f1174]) ).
cnf(s135,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22
| ~ spl0_32 ),
inference(sat_conversion,[],[f1184]) ).
cnf(s139,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_20
| ~ spl0_22
| ~ spl0_32 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s149,plain,
( ~ spl0_7
| ~ spl0_20
| spl0_32 ),
inference(sat_conversion,[],[f1217]) ).
cnf(s151,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s139,s149]) ).
cnf(s152,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_5
| ~ spl0_22 ),
inference(rat,[],[s79,s109]) ).
cnf(s153,plain,
( spl0_18
| ~ spl0_22
| ~ spl0_5 ),
inference(rat,[],[s152,s42,s43]) ).
cnf(s154,plain,
( ~ spl0_22
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s152,s35,s36,s53,s153,s151]) ).
cnf(s155,plain,
( spl0_15
| spl0_22 ),
inference(rat,[],[s92,s79,s19,s20,s21,s22]) ).
cnf(s156,plain,
( ~ spl0_15
| spl0_22
| ~ spl0_7 ),
inference(rat,[],[s92,s79,s12,s13,s14,s15,s61]) ).
cnf(s157,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s156,s155,s154]) ).
cnf(s158,plain,
~ spl0_5,
inference(rat,[],[s92,s79,s152,s5,s6,s7,s8,s157]) ).
cnf(s159,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_4
| ~ spl0_22 ),
inference(rat,[],[s79,s99]) ).
cnf(s160,plain,
( ~ spl0_22
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s159,s14,s15,s113]) ).
cnf(s161,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s156,s155,s160]) ).
cnf(s162,plain,
~ spl0_4,
inference(rat,[],[s92,s79,s159,s5,s6,s7,s8,s161]) ).
cnf(s163,plain,
( ~ spl0_20
| ~ spl0_7
| ~ spl0_22
| ~ spl0_3 ),
inference(rat,[],[s135,s149]) ).
cnf(s164,plain,
( spl0_12
| spl0_20 ),
inference(rat,[],[s53,s35,s42]) ).
cnf(s165,plain,
( spl0_20
| ~ spl0_22
| ~ spl0_3 ),
inference(rat,[],[s53,s36,s43,s102,s164]) ).
cnf(s166,plain,
( ~ spl0_20
| ~ spl0_22
| ~ spl0_3 ),
inference(rat,[],[s102,s7,s8,s163]) ).
cnf(s167,plain,
( ~ spl0_22
| ~ spl0_3 ),
inference(rat,[],[s166,s165]) ).
cnf(s168,plain,
( ~ spl0_15
| spl0_22 ),
inference(rat,[],[s92,s79,s5,s6,s7,s8,s156]) ).
cnf(s169,plain,
spl0_22,
inference(rat,[],[s168,s155]) ).
cnf(s170,plain,
~ spl0_3,
inference(rat,[],[s167,s169]) ).
cnf(s172,plain,
( spl0_18
| spl0_20 ),
inference(rat,[],[s82,s40,s41]) ).
cnf(s173,plain,
( ~ spl0_18
| spl0_20 ),
inference(rat,[],[s82,s33,s34,s53]) ).
cnf(s174,plain,
spl0_20,
inference(rat,[],[s173,s172]) ).
cnf(s175,plain,
~ spl0_2,
inference(rat,[],[s45,s5,s6,s66,s48,s174,s169]) ).
cnf(s176,plain,
spl0_1,
inference(rat,[],[s1,s158,s162,s170,s175]) ).
cnf(s177,plain,
~ spl0_7,
inference(rat,[],[s149,s133,s174,s169,s176]) ).
cnf(s180,plain,
spl0_11,
inference(rat,[],[s6,s177]) ).
cnf(s181,plain,
spl0_10,
inference(rat,[],[s5,s177]) ).
cnf(s187,plain,
$false,
inference(rat,[],[s130,s169,s176,s180,s181]) ).
fof(f1219,plain,
$false,
inference(avatar_sat_refutation,[],[s187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP209-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n010.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 09:38:01 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.48 Running first-order theorem proving
% 0.14/0.48 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.21/2.01 % (703081)Input is clausal, will run a generic CNF schedule.
% 2.21/2.01 % (703092)dis-21_1_sil=8000:lcm=predicate:random_seed=1230626092: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)
% 2.21/2.01 % (703092)Refutation not found, incomplete strategy
% 2.21/2.01 % (703092)------------------------------
% 2.21/2.01 % (703092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/2.01 % (703092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/2.01 % (703092)CaDiCaL version: 2.1.3
% 2.21/2.01 % (703092)Termination reason: Refutation not found, incomplete strategy
% 2.21/2.01 % (703092)Time elapsed: 0.003 s
% 2.21/2.01 % (703092)Peak memory usage: 88 MB
% 2.21/2.01 % (703092)Instructions burned: 2 (million)
% 2.21/2.01 % (703088)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1819181066:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.21/2.01 % (703087)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=116049650:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.21/2.01 % (703086)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=665920455:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.21/2.01 % (703089)lrs+10_1_sil=8000:sp=occurrence:random_seed=2773153392:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.21/2.01 % (703090)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=448150023:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.21/2.01 % (703091)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2009096917:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.21/2.01 % (703091)First to succeed.
% 2.21/2.01 % (703091)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-703081"
% 2.21/2.01 % (703089)Instruction limit reached!
% 2.21/2.01 % (703089)------------------------------
% 2.21/2.01 % (703089)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/2.01 % (703089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/2.01 % (703089)CaDiCaL version: 2.1.3
% 2.21/2.01 % (703089)Termination reason: Instruction limit
% 2.21/2.01 % (703089)Termination phase: Saturation
% 2.21/2.01 % (703089)Time elapsed: 0.096 s
% 2.21/2.01 % (703089)Peak memory usage: 89 MB
% 2.21/2.01 % (703089)Instructions burned: 107 (million)
% 2.21/2.01 % (703090)Instruction limit reached!
% 2.21/2.01 % (703090)------------------------------
% 2.21/2.01 % (703090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.21/2.01 % (703090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/2.01 % (703090)CaDiCaL version: 2.1.3
% 2.21/2.01 % (703090)Termination reason: Instruction limit
% 2.21/2.01 % (703090)Termination phase: Saturation
% 2.21/2.01 % (703090)Time elapsed: 0.105 s
% 2.21/2.01 % (703090)Peak memory usage: 89 MB
% 2.21/2.01 % (703090)Instructions burned: 114 (million)
% 2.21/2.01 % (703092)------------------------------
% 2.21/2.01 % (703092)------------------------------
% 2.21/2.01 % (703101)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2334253078:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 2.21/2.01 % (703100)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=3853518016:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 2.21/2.01 % (703102)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4277331574:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 2.21/2.01 % (703091)Refutation found. Thanks to Tanya!
% 2.21/2.01 % SZS status Unsatisfiable for theBenchmark
% 2.21/2.01 % SZS output start Proof for theBenchmark
% See solution above
% 6.43/2.35 % (703091)------------------------------
% 6.43/2.35 % (703091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.43/2.35 % (703091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.43/2.35 % (703091)CaDiCaL version: 2.1.3
% 6.43/2.35 % (703091)Termination reason: Refutation
% 6.43/2.35 % (703091)Time elapsed: 0.041 s
% 6.43/2.35 % (703091)Peak memory usage: 89 MB
% 6.43/2.35 % (703091)Instructions burned: 39 (million)
% 6.43/2.35 % (703091)------------------------------
% 6.43/2.35 % (703091)------------------------------
% 6.43/2.35 % (703081)Success in time 0.765 s
% 6.43/2.35 % Vampire exiting
%------------------------------------------------------------------------------