%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP354-1 : 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 : n006.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 10:13:43 AM UTC 2026
% Result : Unsatisfiable 2.74s 1.28s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 52
% Syntax : Number of formulae : 285 ( 23 unt; 19 def)
% Number of atoms : 835 ( 282 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 998 ( 448 ~; 531 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 43 !; 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_c8,sk_c7) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f17]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c9
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c9)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c9)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c9)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c9)
| sk_c9 = inverse(sk_c4) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c4,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c9)
| sk_c9 = multiply(sk_c4,sk_c8) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c9) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c9)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c9) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c7 = inverse(sk_c9)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f65]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f73]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f89]) ).
fof(f101,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c7) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c7
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X3) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| multiply(X4,X5) != sk_c8
| inverse(X4) != X5
| multiply(X5,sk_c7) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_49) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4,X5] :
( multiply(sk_c8,sk_c7) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != inverse(sk_c9)
| sk_c8 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c8 != multiply(X5,sk_c7) ),
inference(reorient_equations,[],[f101]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| inverse(X0) != sk_c9
| sk_c7 != inverse(sk_c9)
| sk_c8 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c7) ),
inference(equality_resolution,[],[f102]) ).
fof(f105,definition,
( spl0_1
<=> ! [X4] :
( sk_c8 != multiply(X4,inverse(X4))
| sk_c8 != multiply(inverse(X4),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f106,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c7)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f108,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f109,plain,
( ! [X3] :
( sk_c9 != inverse(X3)
| sk_c9 != multiply(X3,sk_c8) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_3
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f112,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f113,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| spl0_3 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f115,definition,
( spl0_4
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f116,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,definition,
( spl0_5
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f119,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c8 != multiply(X1,sk_c7) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f121,definition,
( spl0_6
<=> sk_c7 = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f122,plain,
( sk_c7 = inverse(sk_c9)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f123,plain,
( sk_c7 != inverse(sk_c9)
| spl0_6 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f125,definition,
( spl0_7
<=> multiply(sk_c8,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f126,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f127,plain,
( multiply(sk_c8,sk_c7) != sk_c9
| spl0_7 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f103,f125,f115,f121,f118,f115,f111,f108,f105]) ).
fof(f134,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f136,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f139,definition,
( spl0_10
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f141,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f144,definition,
( spl0_11
<=> sk_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f146,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f144]) ).
fof(f149,definition,
( spl0_12
<=> sk_c9 = multiply(sk_c4,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f151,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f154,definition,
( spl0_13
<=> sk_c9 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f156,plain,
( sk_c9 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f158,plain,
( spl0_3
| spl0_9 ),
inference(avatar_split_clause,[],[f90,f134,f111]) ).
fof(f160,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f162,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f160]) ).
fof(f165,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c3,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f167,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f165]) ).
fof(f170,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f172,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f178,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f74,f170,f111]) ).
fof(f182,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f66,f121,f139]) ).
fof(f183,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f64,f121,f144]) ).
fof(f184,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f62,f121,f149]) ).
fof(f185,plain,
( spl0_13
| spl0_6 ),
inference(avatar_split_clause,[],[f60,f121,f154]) ).
fof(f186,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f58,f121,f111]) ).
fof(f187,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f56,f121,f160]) ).
fof(f188,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f54,f121,f165]) ).
fof(f190,definition,
( spl0_17
<=> sk_c9 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f192,plain,
( sk_c9 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f194,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f50,f190,f139]) ).
fof(f195,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f48,f190,f144]) ).
fof(f196,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f46,f190,f149]) ).
fof(f197,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f44,f190,f154]) ).
fof(f198,plain,
( spl0_3
| spl0_17 ),
inference(avatar_split_clause,[],[f42,f190,f111]) ).
fof(f199,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f40,f190,f160]) ).
fof(f200,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f38,f190,f165]) ).
fof(f202,definition,
( spl0_18
<=> sk_c8 = multiply(sk_c1,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f204,plain,
( sk_c8 = multiply(sk_c1,sk_c9)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f206,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f202,f139]) ).
fof(f207,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f202,f144]) ).
fof(f208,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f30,f202,f149]) ).
fof(f209,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f28,f202,f154]) ).
fof(f210,plain,
( spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f26,f202,f111]) ).
fof(f211,plain,
( spl0_14
| spl0_18 ),
inference(avatar_split_clause,[],[f24,f202,f160]) ).
fof(f212,plain,
( spl0_15
| spl0_18 ),
inference(avatar_split_clause,[],[f22,f202,f165]) ).
fof(f214,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f18,f125,f139]) ).
fof(f215,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f16,f125,f144]) ).
fof(f216,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f14,f125,f149]) ).
fof(f217,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f12,f125,f154]) ).
fof(f219,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f8,f125,f160]) ).
fof(f220,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f6,f125,f165]) ).
fof(f221,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_10 ),
inference(superposition,[],[f3,f141]) ).
fof(f222,plain,
( identity = multiply(sk_c9,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f156]) ).
fof(f223,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f162]) ).
fof(f225,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f230,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c9,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f167]) ).
fof(f233,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f225,f1]) ).
fof(f235,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f221]) ).
fof(f236,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f235,f1]) ).
fof(f237,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c9,multiply(sk_c4,X0))
| ~ spl0_13 ),
inference(superposition,[],[f4,f222]) ).
fof(f238,plain,
( ! [X0] : multiply(sk_c9,multiply(sk_c4,X0)) = X0
| ~ spl0_13 ),
inference(forward_demodulation,[],[f237,f1]) ).
fof(f244,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f236,f146]) ).
fof(f255,plain,
( sk_c8 = multiply(sk_c9,sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f238,f151]) ).
fof(f260,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c3,sk_c8)
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[],[f230,f112]) ).
fof(f296,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f233,f244]) ).
fof(f298,plain,
( sk_c7 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_3 ),
inference(superposition,[],[f233,f112]) ).
fof(f302,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl0_14 ),
inference(superposition,[],[f233,f223]) ).
fof(f303,plain,
( sk_c4 = multiply(inverse(sk_c9),identity)
| ~ spl0_13 ),
inference(superposition,[],[f233,f222]) ).
fof(f311,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f296,f3]) ).
fof(f316,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f311]) ).
fof(f329,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f302,f311]) ).
fof(f330,plain,
( sk_c7 = sk_c3
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f329,f298]) ).
fof(f333,plain,
( sk_c8 = multiply(sk_c7,sk_c9)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f167,f330]) ).
fof(f334,plain,
( sk_c9 = inverse(sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f162,f330]) ).
fof(f337,plain,
( sk_c4 = multiply(inverse(sk_c9),sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f303,f311]) ).
fof(f338,plain,
( sk_c7 = sk_c4
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f337,f298]) ).
fof(f342,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f151,f338]) ).
fof(f359,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f260,f330]) ).
fof(f360,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f359,f316]) ).
fof(f401,plain,
( sk_c7 = sk_c9
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f342,f360]) ).
fof(f420,plain,
( sk_c9 = inverse(sk_c9)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f334,f401]) ).
fof(f431,plain,
( sk_c7 != sk_c9
| ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f123,f420]) ).
fof(f435,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f431,f401]) ).
fof(f436,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f439,plain,
( sk_c7 != sk_c9
| spl0_7
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f127,f316]) ).
fof(f440,plain,
( $false
| ~ spl0_3
| spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f439,f401]) ).
fof(f441,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f440]) ).
fof(f446,plain,
( ! [X4] :
( sk_c8 != multiply(inverse(X4),sk_c9)
| sk_c8 != multiply(X4,inverse(X4)) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f106,f401]) ).
fof(f450,plain,
( sk_c8 != multiply(sk_c9,sk_c9)
| sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f446,f156]) ).
fof(f456,plain,
( sk_c8 != multiply(sk_c4,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f450,f255]) ).
fof(f463,plain,
( sk_c8 != multiply(sk_c7,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f456,f338]) ).
fof(f472,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f463,f333]) ).
fof(f473,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f472]) ).
fof(f478,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f109,f156]) ).
fof(f480,plain,
( sk_c9 != multiply(sk_c4,sk_c8)
| ~ spl0_2
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f478]) ).
fof(f485,plain,
( $false
| ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f480,f151]) ).
fof(f486,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f499,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_4
| ~ spl0_14 ),
inference(superposition,[],[f116,f162]) ).
fof(f503,plain,
( sk_c8 != multiply(sk_c3,sk_c9)
| ~ spl0_4
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f499]) ).
fof(f508,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f503,f167]) ).
fof(f509,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f545,plain,
( sk_c9 != sk_c9
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f116,f192]) ).
fof(f547,plain,
( identity = multiply(sk_c9,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f192]) ).
fof(f548,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f545]) ).
fof(f550,plain,
( ~ spl0_18
| ~ spl0_4
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f548,f190,f115,f202]) ).
fof(f567,plain,
( sk_c9 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_18 ),
inference(superposition,[],[f233,f204]) ).
fof(f568,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c9,X0))
| ~ spl0_18 ),
inference(superposition,[],[f4,f204]) ).
fof(f570,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f567,f192]) ).
fof(f649,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c8)
| ~ spl0_16 ),
inference(superposition,[],[f233,f172]) ).
fof(f651,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_9
| ~ spl0_16 ),
inference(forward_demodulation,[],[f649,f136]) ).
fof(f653,plain,
( sk_c1 = multiply(inverse(sk_c9),identity)
| ~ spl0_17 ),
inference(superposition,[],[f233,f547]) ).
fof(f656,plain,
( sk_c1 = multiply(sk_c7,identity)
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f653,f122]) ).
fof(f660,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_1
| ~ spl0_17 ),
inference(superposition,[],[f106,f192]) ).
fof(f668,definition,
( spl0_22
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f669,plain,
( identity = sk_c8
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f673,plain,
( sk_c8 != multiply(sk_c1,sk_c9)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f660,f112]) ).
fof(f677,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f673,f204]) ).
fof(f678,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f677]) ).
fof(f685,plain,
( sk_c9 != sk_c9
| sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_17 ),
inference(superposition,[],[f109,f192]) ).
fof(f687,plain,
( sk_c9 != multiply(sk_c1,sk_c8)
| ~ spl0_2
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f685]) ).
fof(f699,definition,
( spl0_25
<=> sk_c9 = multiply(sk_c9,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f700,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f715,plain,
( spl0_25
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f570,f202,f190,f699]) ).
fof(f717,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_25 ),
inference(superposition,[],[f233,f700]) ).
fof(f719,plain,
( identity = sk_c8
| ~ spl0_25 ),
inference(forward_demodulation,[],[f717,f3]) ).
fof(f721,plain,
( spl0_22
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f719,f699,f668]) ).
fof(f726,plain,
( multiply(sk_c8,sk_c7) = multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f568,f112]) ).
fof(f735,plain,
( sk_c9 = multiply(sk_c1,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f726,f126]) ).
fof(f738,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f735,f687]) ).
fof(f739,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f738]) ).
fof(f744,plain,
( sk_c7 != sk_c7
| sk_c8 != multiply(sk_c9,sk_c7)
| ~ spl0_5
| ~ spl0_6 ),
inference(superposition,[],[f119,f122]) ).
fof(f750,plain,
( sk_c8 != multiply(sk_c9,sk_c7)
| ~ spl0_5
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f744]) ).
fof(f754,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f750,f112]) ).
fof(f755,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f796,plain,
( sk_c1 = multiply(sk_c7,sk_c8)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f656,f669]) ).
fof(f797,plain,
( sk_c7 = sk_c1
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f796,f651]) ).
fof(f807,plain,
( identity = multiply(sk_c9,sk_c7)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(superposition,[],[f547,f797]) ).
fof(f811,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_demodulation,[],[f807,f669]) ).
fof(f812,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f811,f113]) ).
fof(f813,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f812]) ).
cnf(s1,plain,
( spl0_4
| spl0_2
| ~ spl0_3
| spl0_1
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f128]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6
| ~ spl0_7 ),
inference(rat,[],[s1]) ).
cnf(s8,plain,
( spl0_3
| spl0_9 ),
inference(sat_conversion,[],[f158]) ).
cnf(s16,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f178]) ).
cnf(s20,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f182]) ).
cnf(s21,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f183]) ).
cnf(s22,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f184]) ).
cnf(s23,plain,
( spl0_6
| spl0_13 ),
inference(sat_conversion,[],[f185]) ).
cnf(s24,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f186]) ).
cnf(s25,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f187]) ).
cnf(s26,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f188]) ).
cnf(s28,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f194]) ).
cnf(s29,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f195]) ).
cnf(s30,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f196]) ).
cnf(s31,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f197]) ).
cnf(s32,plain,
( spl0_3
| spl0_17 ),
inference(sat_conversion,[],[f198]) ).
cnf(s33,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f199]) ).
cnf(s34,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f200]) ).
cnf(s36,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f206]) ).
cnf(s37,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f207]) ).
cnf(s38,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f208]) ).
cnf(s39,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f209]) ).
cnf(s40,plain,
( spl0_3
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s41,plain,
( spl0_14
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s42,plain,
( spl0_15
| spl0_18 ),
inference(sat_conversion,[],[f212]) ).
cnf(s44,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f214]) ).
cnf(s45,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f215]) ).
cnf(s46,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f216]) ).
cnf(s47,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f217]) ).
cnf(s49,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f219]) ).
cnf(s50,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f220]) ).
cnf(s51,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f436]) ).
cnf(s52,plain,
( ~ spl0_3
| spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s59,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f473]) ).
cnf(s60,plain,
( ~ spl0_2
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f486]) ).
cnf(s65,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f509]) ).
cnf(s71,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f550]) ).
cnf(s82,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f678]) ).
cnf(s85,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_25 ),
inference(sat_conversion,[],[f715]) ).
cnf(s86,plain,
( spl0_22
| ~ spl0_25 ),
inference(sat_conversion,[],[f721]) ).
cnf(s87,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f739]) ).
cnf(s89,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f755]) ).
cnf(s93,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22 ),
inference(sat_conversion,[],[f813]) ).
cnf(s94,plain,
spl0_3,
inference(rat,[],[s86,s93,s85,s8,s16,s24,s32,s40]) ).
cnf(s95,plain,
spl0_7,
inference(rat,[],[s52,s44,s45,s46,s47,s49,s50,s94]) ).
cnf(s96,plain,
spl0_6,
inference(rat,[],[s51,s20,s21,s22,s23,s25,s26,s94]) ).
cnf(s97,plain,
~ spl0_5,
inference(rat,[],[s89,s94,s96]) ).
cnf(s98,plain,
( spl0_15
| ~ spl0_4 ),
inference(rat,[],[s71,s34,s42]) ).
cnf(s99,plain,
( ~ spl0_15
| ~ spl0_4 ),
inference(rat,[],[s71,s33,s41,s65]) ).
cnf(s100,plain,
~ spl0_4,
inference(rat,[],[s99,s98]) ).
cnf(s102,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s60,s38,s39]) ).
cnf(s103,plain,
( ~ spl0_18
| ~ spl0_2 ),
inference(rat,[],[s60,s30,s31,s87,s95,s94]) ).
cnf(s104,plain,
~ spl0_2,
inference(rat,[],[s103,s102]) ).
cnf(s105,plain,
spl0_1,
inference(rat,[],[s2,s94,s96,s97,s95,s100,s104]) ).
cnf(s106,plain,
spl0_18,
inference(rat,[],[s59,s36,s37,s38,s39,s41,s42,s105,s94]) ).
cnf(s107,plain,
~ spl0_17,
inference(rat,[],[s82,s105,s94,s106]) ).
cnf(s108,plain,
spl0_15,
inference(rat,[],[s34,s107]) ).
cnf(s109,plain,
spl0_14,
inference(rat,[],[s33,s107]) ).
cnf(s110,plain,
spl0_13,
inference(rat,[],[s31,s107]) ).
cnf(s111,plain,
spl0_12,
inference(rat,[],[s30,s107]) ).
cnf(s112,plain,
spl0_11,
inference(rat,[],[s29,s107]) ).
cnf(s113,plain,
spl0_10,
inference(rat,[],[s28,s107]) ).
cnf(s116,plain,
$false,
inference(rat,[],[s59,s108,s109,s110,s111,s94,s105,s112,s113]) ).
fof(f814,plain,
$false,
inference(avatar_sat_refutation,[],[s116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP354-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 27 09:54:56 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 2.74/1.28 % (2745894)Input is clausal, will run a generic CNF schedule.
% 2.74/1.28 % (2745914)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=980246888:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.28 % (2745915)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1153891982:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.28 % (2745917)lrs+10_1_sil=8000:sp=occurrence:random_seed=1676844698:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.28 % (2745919)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2087454415:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.28 % (2745920)dis-21_1_sil=8000:lcm=predicate:random_seed=439062951: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)
% 2.74/1.28 % (2745918)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1540392519:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.28 % (2745920)Refutation not found, incomplete strategy
% 2.74/1.28 % (2745920)------------------------------
% 2.74/1.28 % (2745920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2745920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2745920)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2745920)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2745920)Time elapsed: 0.002 s
% 2.74/1.28 % (2745920)Peak memory usage: 88 MB
% 2.74/1.28 % (2745920)Instructions burned: 2 (million)
% 2.74/1.28 % (2745917)Refutation not found, incomplete strategy
% 2.74/1.28 % (2745917)------------------------------
% 2.74/1.28 % (2745917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2745917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2745917)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2745917)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2745917)Time elapsed: 0.004 s
% 2.74/1.28 % (2745917)Peak memory usage: 88 MB
% 2.74/1.28 % (2745917)Instructions burned: 5 (million)
% 2.74/1.28 % (2745919)First to succeed.
% 2.74/1.28 % (2745919)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2745894"
% 2.74/1.28 % (2745916)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1925986725:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.28 % (2745918)Instruction limit reached!
% 2.74/1.28 % (2745918)------------------------------
% 2.74/1.28 % (2745918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2745918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2745918)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2745918)Termination reason: Instruction limit
% 2.74/1.28 % (2745918)Termination phase: Saturation
% 2.74/1.28 % (2745918)Time elapsed: 0.066 s
% 2.74/1.28 % (2745918)Peak memory usage: 89 MB
% 2.74/1.28 % (2745918)Instructions burned: 114 (million)
% 2.74/1.28 % (2745929)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=1569899834:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.74/1.28 % (2745929)Refutation not found, incomplete strategy
% 2.74/1.28 % (2745929)------------------------------
% 2.74/1.28 % (2745929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.28 % (2745929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.28 % (2745929)CaDiCaL version: 2.1.3
% 2.74/1.28 % (2745929)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.28 % (2745929)Time elapsed: 0.004 s
% 2.74/1.28 % (2745929)Peak memory usage: 88 MB
% 2.74/1.28 % (2745929)Instructions burned: 5 (million)
% 2.74/1.28 % (2745920)------------------------------
% 2.74/1.28 % (2745920)------------------------------
% 2.74/1.28 % (2745917)------------------------------
% 2.74/1.28 % (2745917)------------------------------
% 2.74/1.28 % (2745919)Refutation found. Thanks to Tanya!
% 2.74/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.48 % (2745919)------------------------------
% 3.55/1.48 % (2745919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.48 % (2745919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.48 % (2745919)CaDiCaL version: 2.1.3
% 3.55/1.48 % (2745919)Termination reason: Refutation
% 3.55/1.48 % (2745919)Time elapsed: 0.019 s
% 3.55/1.48 % (2745919)Peak memory usage: 90 MB
% 3.55/1.48 % (2745919)Instructions burned: 28 (million)
% 3.55/1.48 % (2745919)------------------------------
% 3.55/1.48 % (2745919)------------------------------
% 3.55/1.48 % (2745894)Success in time 0.419 s
% 3.55/1.48 % Vampire exiting
%------------------------------------------------------------------------------