%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP375-1 : 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 : n008.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 10:13:47 AM UTC 2026
% Result : Unsatisfiable 3.30s 1.32s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 46
% Syntax : Number of formulae : 342 ( 21 unt; 19 def)
% Number of atoms : 1300 ( 363 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1873 ( 915 ~; 939 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 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 : 77 ( 0 sgn 77 !; 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,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( inverse(sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f7]) ).
fof(f10,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c10) = sk_c9
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c10) = sk_c9
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = inverse(sk_c1)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(sk_c8,sk_c10) != sk_c9
| multiply(X1,sk_c10) != sk_c9
| inverse(X1) != sk_c10
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c9
| multiply(X3,X4) != sk_c10
| inverse(X3) != X4
| multiply(X4,sk_c9) != sk_c10
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,X4)
| inverse(X3) != X4
| sk_c10 != multiply(X4,sk_c9)
| inverse(X5) != X6
| inverse(X6) != X4
| multiply(X5,X4) != X6 ),
inference(reorient_equations,[],[f83]) ).
fof(f85,plain,
! [X2,X3,X0,X1,X6,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X5) != X6
| inverse(X3) != inverse(X6)
| multiply(X5,inverse(X3)) != X6 ),
inference(equality_resolution,[],[f84]) ).
fof(f86,plain,
! [X2,X3,X0,X1,X5] :
( inverse(sk_c10) != sk_c9
| sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c9 != multiply(sk_c8,sk_c10)
| sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1)
| sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2)
| sk_c10 != multiply(X3,inverse(X3))
| sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X3) != inverse(inverse(X5))
| inverse(X5) != multiply(X5,inverse(X3)) ),
inference(equality_resolution,[],[f85]) ).
fof(f88,definition,
( spl0_1
<=> ! [X5,X3] :
( sk_c10 != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(inverse(X3),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f89,plain,
( ! [X3,X5] :
( sk_c10 != multiply(inverse(X3),sk_c9)
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5))
| sk_c10 != multiply(X3,inverse(X3)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f91,definition,
( spl0_2
<=> ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f92,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c9)
| sk_c9 != inverse(X2) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,definition,
( spl0_3
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f95,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,definition,
( spl0_4
<=> sk_c9 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f98,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c9 != multiply(sk_c8,sk_c10)
| spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f101,definition,
( spl0_5
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f102,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f103,plain,
( inverse(sk_c10) != sk_c9
| spl0_5 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f86,f101,f94,f97,f94,f91,f88]) ).
fof(f126,definition,
( spl0_10
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f128,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f129,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f74,f97,f126]) ).
fof(f131,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f133,plain,
( sk_c10 = multiply(sk_c4,sk_c7)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f72,f97,f131]) ).
fof(f136,definition,
( spl0_12
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f138,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f70,f97,f136]) ).
fof(f141,definition,
( spl0_13
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f143,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( spl0_13
| spl0_4 ),
inference(avatar_split_clause,[],[f68,f97,f141]) ).
fof(f146,definition,
( spl0_14
<=> sk_c10 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f148,plain,
( sk_c10 = inverse(sk_c2)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( spl0_14
| spl0_4 ),
inference(avatar_split_clause,[],[f66,f97,f146]) ).
fof(f151,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c2,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f152,plain,
( sk_c9 != multiply(sk_c2,sk_c10)
| spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( sk_c9 = multiply(sk_c2,sk_c10)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( spl0_15
| spl0_4 ),
inference(avatar_split_clause,[],[f64,f97,f151]) ).
fof(f156,definition,
( spl0_16
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f158,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f163,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f54,f156,f126]) ).
fof(f164,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f52,f156,f131]) ).
fof(f165,plain,
( spl0_12
| spl0_16 ),
inference(avatar_split_clause,[],[f50,f156,f136]) ).
fof(f166,plain,
( spl0_13
| spl0_16 ),
inference(avatar_split_clause,[],[f48,f156,f141]) ).
fof(f167,plain,
( spl0_14
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f156,f146]) ).
fof(f168,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f44,f156,f151]) ).
fof(f170,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c1,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f172,plain,
( sk_c9 = multiply(sk_c1,sk_c10)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f177,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f34,f170,f126]) ).
fof(f178,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f170,f131]) ).
fof(f179,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f170,f136]) ).
fof(f180,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f170,f141]) ).
fof(f181,plain,
( spl0_14
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f170,f146]) ).
fof(f182,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f170,f151]) ).
fof(f187,plain,
( spl0_10
| spl0_5 ),
inference(avatar_split_clause,[],[f15,f101,f126]) ).
fof(f188,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f13,f101,f131]) ).
fof(f189,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f11,f101,f136]) ).
fof(f191,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f8,f101,f146]) ).
fof(f192,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f6,f101,f151]) ).
fof(f193,plain,
( identity = multiply(sk_c10,sk_c2)
| ~ spl0_14 ),
inference(superposition,[],[f3,f148]) ).
fof(f194,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f3,f138]) ).
fof(f200,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f202,plain,
( ! [X0] : multiply(sk_c3,multiply(sk_c9,X0)) = multiply(sk_c8,X0)
| ~ spl0_13 ),
inference(superposition,[],[f4,f143]) ).
fof(f206,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f200,f1]) ).
fof(f209,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c10,multiply(sk_c2,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f193]) ).
fof(f210,plain,
( ! [X0] : multiply(sk_c10,multiply(sk_c2,X0)) = X0
| ~ spl0_14 ),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f223,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f210,f153]) ).
fof(f228,plain,
( multiply(sk_c8,sk_c3) = multiply(sk_c3,identity)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f202,f194]) ).
fof(f270,plain,
( sk_c2 = multiply(inverse(sk_c10),identity)
| ~ spl0_14 ),
inference(superposition,[],[f206,f193]) ).
fof(f272,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f206,f223]) ).
fof(f273,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl0_12 ),
inference(superposition,[],[f206,f194]) ).
fof(f277,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f206,f143]) ).
fof(f280,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_11 ),
inference(superposition,[],[f206,f133]) ).
fof(f297,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f280,f128]) ).
fof(f300,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f277,f138]) ).
fof(f304,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f272,f3]) ).
fof(f318,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f297]) ).
fof(f320,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f318,f3]) ).
fof(f323,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f320,f304]) ).
fof(f328,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f206,f300]) ).
fof(f330,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f328,f3]) ).
fof(f333,plain,
( sk_c9 = sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f330,f304]) ).
fof(f336,plain,
( sk_c9 != multiply(sk_c9,sk_c10)
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f99,f333]) ).
fof(f356,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f273,f304]) ).
fof(f357,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f356,f3]) ).
fof(f358,plain,
( sk_c9 = sk_c3
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f357,f304]) ).
fof(f359,plain,
( sk_c10 = sk_c3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f358,f323]) ).
fof(f363,plain,
( inverse(sk_c10) = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f138,f359]) ).
fof(f364,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f363,f323]) ).
fof(f465,plain,
( multiply(sk_c3,sk_c9) = multiply(sk_c8,sk_c3)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f228,f304]) ).
fof(f466,plain,
( multiply(sk_c8,sk_c10) = multiply(sk_c10,sk_c9)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f465,f359]) ).
fof(f467,plain,
( sk_c10 = multiply(sk_c8,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f466,f223]) ).
fof(f468,plain,
( sk_c10 = multiply(sk_c9,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f467,f333]) ).
fof(f469,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f468,f323]) ).
fof(f556,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f336,f323]) ).
fof(f557,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f556,f469]) ).
fof(f558,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f560,plain,
( sk_c10 != inverse(sk_c10)
| spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f103,f323]) ).
fof(f562,plain,
( $false
| spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f560,f364]) ).
fof(f563,plain,
( spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f562]) ).
fof(f564,plain,
( ! [X3,X5] :
( sk_c10 != multiply(inverse(X3),sk_c10)
| sk_c10 != multiply(X3,inverse(X3))
| inverse(X5) != multiply(X5,inverse(X3))
| inverse(X3) != inverse(inverse(X5)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f89,f323]) ).
fof(f568,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c2,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f564,f148]) ).
fof(f583,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c2,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f568,f469]) ).
fof(f592,plain,
( ! [X0] :
( sk_c10 != sk_c9
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f583,f153]) ).
fof(f600,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f592,f323]) ).
fof(f631,plain,
( sk_c10 != inverse(sk_c9)
| sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f600,f138]) ).
fof(f638,plain,
( sk_c10 != inverse(sk_c10)
| sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f631,f323]) ).
fof(f645,plain,
( sk_c9 != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f638,f364]) ).
fof(f653,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f645,f359]) ).
fof(f661,plain,
( sk_c10 != sk_c9
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f653,f469]) ).
fof(f668,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f661,f323]) ).
fof(f669,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f668]) ).
fof(f670,plain,
( ! [X1] :
( sk_c10 != inverse(X1)
| sk_c10 != multiply(X1,sk_c10) )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f95,f323]) ).
fof(f674,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f670,f148]) ).
fof(f679,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f674]) ).
fof(f685,plain,
( sk_c10 != sk_c9
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f679,f153]) ).
fof(f694,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f685,f323]) ).
fof(f695,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f694]) ).
fof(f704,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f92,f323]) ).
fof(f705,plain,
( ! [X2] :
( sk_c9 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f704,f333]) ).
fof(f706,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f705,f323]) ).
fof(f707,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c10 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f706,f323]) ).
fof(f711,plain,
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f707,f138]) ).
fof(f720,plain,
( sk_c10 != multiply(sk_c3,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f711,f323]) ).
fof(f729,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f720,f359]) ).
fof(f738,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f729,f469]) ).
fof(f739,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f738]) ).
fof(f756,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f158]) ).
fof(f974,definition,
( spl0_19
<=> sk_c10 = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f975,plain,
( sk_c10 = inverse(sk_c8)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f976,plain,
( sk_c10 != inverse(sk_c8)
| spl0_19 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1153,plain,
( sk_c2 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f270,f320]) ).
fof(f1157,plain,
( sk_c10 = multiply(sk_c10,sk_c1)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f756,f320]) ).
fof(f1159,plain,
( identity = sk_c2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1153,f3]) ).
fof(f1160,plain,
( sk_c10 = sk_c2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f1159,f320]) ).
fof(f1163,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f148,f1160]) ).
fof(f1166,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f3,f102]) ).
fof(f1169,plain,
( ! [X0] : multiply(sk_c9,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl0_4 ),
inference(superposition,[],[f4,f98]) ).
fof(f1171,plain,
( identity = multiply(sk_c10,sk_c8)
| ~ spl0_19 ),
inference(superposition,[],[f3,f975]) ).
fof(f1172,plain,
( sk_c10 = multiply(sk_c10,sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1171,f320]) ).
fof(f1173,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14 ),
inference(superposition,[],[f1163,f102]) ).
fof(f1178,plain,
( sk_c9 != multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f152,f1160]) ).
fof(f1184,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f1178,f1173]) ).
fof(f1188,plain,
( sk_c1 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f206,f1157]) ).
fof(f1190,plain,
( identity = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1188,f3]) ).
fof(f1191,plain,
( sk_c10 = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1190,f320]) ).
fof(f1193,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f1157,f1191]) ).
fof(f1195,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f158,f1191]) ).
fof(f1198,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f1193,f1184]) ).
fof(f1199,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f1198]) ).
fof(f1200,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f172,f1191]) ).
fof(f1201,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f1195,f102]) ).
fof(f1210,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1200,f1201]) ).
fof(f1212,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c10,X0))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f4,f1210]) ).
fof(f1245,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f92,f1201]) ).
fof(f1246,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1245,f1201]) ).
fof(f1257,plain,
( sk_c10 != sk_c10
| sk_c8 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f1246,f158]) ).
fof(f1258,plain,
( sk_c8 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f1257]) ).
fof(f1261,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1258,f1191]) ).
fof(f1270,plain,
( sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1261,f1210]) ).
fof(f1273,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(forward_demodulation,[],[f1169,f1201]) ).
fof(f1277,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f206,f1212]) ).
fof(f1280,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1277,f206]) ).
fof(f1284,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16 ),
inference(superposition,[],[f206,f1273]) ).
fof(f1315,plain,
( sk_c10 = sk_c8
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f1172,f1280]) ).
fof(f1316,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f1315,f1270]) ).
fof(f1317,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f1316]) ).
fof(f1318,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1284,f1280]) ).
fof(f1326,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f1318,f3]) ).
fof(f1328,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(superposition,[],[f3,f1318]) ).
fof(f1332,plain,
( sk_c10 = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1328,f320]) ).
fof(f1333,plain,
( sk_c10 = sk_c8
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1326,f320]) ).
fof(f1336,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1333,f1270]) ).
fof(f1337,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1336]) ).
fof(f1340,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_19 ),
inference(superposition,[],[f976,f1332]) ).
fof(f1349,plain,
( $false
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f1340,f1195]) ).
fof(f1350,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f1349]) ).
fof(f1450,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f206,f172]) ).
fof(f1452,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1450,f158]) ).
fof(f1461,plain,
( sk_c9 != sk_c9
| sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_17 ),
inference(superposition,[],[f95,f172]) ).
fof(f1462,plain,
( sk_c10 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1461]) ).
fof(f1464,plain,
( $false
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1462,f158]) ).
fof(f1465,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1464]) ).
fof(f1474,definition,
( spl0_40
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_40])],[avatar_definition]) ).
fof(f1475,plain,
( sk_c10 = sk_c9
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f1479,definition,
( spl0_41
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_41])],[avatar_definition]) ).
fof(f1480,plain,
( identity = sk_c9
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1479]) ).
fof(f1496,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c9)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0))
| sk_c10 != multiply(sk_c1,sk_c10) )
| ~ spl0_1
| ~ spl0_16 ),
inference(superposition,[],[f89,f158]) ).
fof(f1506,definition,
( spl0_45
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f1507,plain,
( identity = sk_c10
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1506]) ).
fof(f1510,plain,
( ! [X0] :
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c10,sk_c9)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1496,f172]) ).
fof(f1518,definition,
( spl0_47
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1519,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f1530,definition,
( spl0_50
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f1531,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1530]) ).
fof(f1532,plain,
( spl0_50
| ~ spl0_47
| ~ spl0_40
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1510,f170,f156,f88,f1474,f1518,f1530]) ).
fof(f1535,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),multiply(sk_c9,X0))
| ~ spl0_4 ),
inference(superposition,[],[f206,f1169]) ).
fof(f1542,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1452,f170,f156,f1518]) ).
fof(f1544,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_47 ),
inference(superposition,[],[f206,f1519]) ).
fof(f1546,plain,
( identity = sk_c9
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1544,f3]) ).
fof(f1548,plain,
( spl0_41
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f1546,f1518,f1479]) ).
fof(f1550,plain,
( ! [X0] : multiply(sk_c9,X0) = X0
| ~ spl0_41 ),
inference(superposition,[],[f1,f1480]) ).
fof(f1582,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_41 ),
inference(superposition,[],[f1166,f1550]) ).
fof(f1591,plain,
( spl0_45
| ~ spl0_5
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f1582,f1479,f101,f1506]) ).
fof(f1594,plain,
( sk_c10 = sk_c9
| ~ spl0_41
| ~ spl0_45 ),
inference(superposition,[],[f1480,f1507]) ).
fof(f1595,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_45 ),
inference(superposition,[],[f1,f1507]) ).
fof(f1602,plain,
( spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f1594,f1506,f1479,f1474]) ).
fof(f1638,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_16
| ~ spl0_50 ),
inference(superposition,[],[f1531,f158]) ).
fof(f1639,plain,
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_50 ),
inference(forward_demodulation,[],[f1638,f102]) ).
fof(f1644,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_5
| ~ spl0_16
| ~ spl0_40
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f1639,f1475]) ).
fof(f1647,plain,
( sk_c10 != sk_c9
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_50 ),
inference(forward_demodulation,[],[f1644,f172]) ).
fof(f1650,plain,
( $false
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f1647,f1475]) ).
fof(f1651,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_50 ),
inference(avatar_contradiction_clause,[],[f1650]) ).
fof(f1655,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_40 ),
inference(forward_demodulation,[],[f92,f1475]) ).
fof(f1656,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1655,f1475]) ).
fof(f1668,plain,
( sk_c10 != sk_c10
| sk_c8 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_40 ),
inference(superposition,[],[f1656,f158]) ).
fof(f1669,plain,
( sk_c8 != multiply(sk_c1,sk_c10)
| ~ spl0_2
| ~ spl0_16
| ~ spl0_40 ),
inference(trivial_inequality_removal,[],[f1668]) ).
fof(f1672,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1669,f172]) ).
fof(f1675,plain,
( sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40 ),
inference(forward_demodulation,[],[f1672,f1475]) ).
fof(f1758,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_4
| ~ spl0_41 ),
inference(forward_demodulation,[],[f1535,f1550]) ).
fof(f1759,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_41
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1758,f1595]) ).
fof(f1763,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_41
| ~ spl0_45 ),
inference(superposition,[],[f1759,f3]) ).
fof(f1770,plain,
( sk_c9 = sk_c8
| ~ spl0_4
| ~ spl0_41
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1763,f1480]) ).
fof(f1772,plain,
( sk_c10 = sk_c8
| ~ spl0_4
| ~ spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1770,f1475]) ).
fof(f1775,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1772,f1675]) ).
fof(f1776,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(avatar_contradiction_clause,[],[f1775]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f104]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f129]) ).
cnf(s8,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f134]) ).
cnf(s9,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f139]) ).
cnf(s10,plain,
( spl0_4
| spl0_13 ),
inference(sat_conversion,[],[f144]) ).
cnf(s11,plain,
( spl0_4
| spl0_14 ),
inference(sat_conversion,[],[f149]) ).
cnf(s12,plain,
( spl0_4
| spl0_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s17,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f163]) ).
cnf(s18,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f164]) ).
cnf(s19,plain,
( spl0_12
| spl0_16 ),
inference(sat_conversion,[],[f165]) ).
cnf(s20,plain,
( spl0_13
| spl0_16 ),
inference(sat_conversion,[],[f166]) ).
cnf(s21,plain,
( spl0_14
| spl0_16 ),
inference(sat_conversion,[],[f167]) ).
cnf(s22,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f168]) ).
cnf(s27,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f177]) ).
cnf(s28,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f178]) ).
cnf(s29,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f179]) ).
cnf(s30,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s31,plain,
( spl0_14
| spl0_17 ),
inference(sat_conversion,[],[f181]) ).
cnf(s32,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f182]) ).
cnf(s37,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f187]) ).
cnf(s38,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f188]) ).
cnf(s39,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f189]) ).
cnf(s41,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f191]) ).
cnf(s42,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f192]) ).
cnf(s43,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f558]) ).
cnf(s44,plain,
( spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f563]) ).
cnf(s51,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f669]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f695]) ).
cnf(s65,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f739]) ).
cnf(s91,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f1199]) ).
cnf(s99,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_19 ),
inference(sat_conversion,[],[f1317]) ).
cnf(s101,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1337]) ).
cnf(s102,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| spl0_19 ),
inference(sat_conversion,[],[f1350]) ).
cnf(s110,plain,
( ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f1465]) ).
cnf(s117,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_47
| spl0_50 ),
inference(sat_conversion,[],[f1532]) ).
cnf(s120,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_47 ),
inference(sat_conversion,[],[f1542]) ).
cnf(s121,plain,
( spl0_41
| ~ spl0_47 ),
inference(sat_conversion,[],[f1548]) ).
cnf(s124,plain,
( ~ spl0_5
| ~ spl0_41
| spl0_45 ),
inference(sat_conversion,[],[f1591]) ).
cnf(s131,plain,
( spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(sat_conversion,[],[f1602]) ).
cnf(s139,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_50 ),
inference(sat_conversion,[],[f1651]) ).
cnf(s145,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17
| ~ spl0_40
| ~ spl0_41
| ~ spl0_45 ),
inference(sat_conversion,[],[f1776]) ).
cnf(s146,plain,
spl0_4,
inference(rat,[],[s43,s7,s8,s9,s10,s11,s12]) ).
cnf(s147,plain,
spl0_5,
inference(rat,[],[s44,s37,s38,s39,s41,s42]) ).
cnf(s148,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_3
| ~ spl0_10 ),
inference(rat,[],[s91,s22,s54,s147]) ).
cnf(s149,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s110,s21,s31]) ).
cnf(s150,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s110,s18,s28]) ).
cnf(s151,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s110,s17,s27,s148]) ).
cnf(s152,plain,
~ spl0_3,
inference(rat,[],[s151,s150,s149]) ).
cnf(s153,plain,
( ~ spl0_16
| ~ spl0_14
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s65,s29,s30,s91,s101,s147,s146]) ).
cnf(s154,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_2
| ~ spl0_10 ),
inference(rat,[],[s65,s19,s20,s22,s153]) ).
cnf(s155,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s99,s102,s21,s31,s154,s146,s147]) ).
cnf(s156,plain,
( ~ spl0_41
| ~ spl0_45
| ~ spl0_2
| ~ spl0_16
| ~ spl0_17 ),
inference(rat,[],[s131,s145,s146]) ).
cnf(s157,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s156,s124,s121,s120,s18,s28,s147]) ).
cnf(s158,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s156,s124,s121,s120,s17,s27,s155,s147]) ).
cnf(s159,plain,
~ spl0_2,
inference(rat,[],[s158,s157]) ).
cnf(s160,plain,
spl0_1,
inference(rat,[],[s2,s147,s146,s152,s159]) ).
cnf(s162,plain,
( ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s117,s139,s131,s124,s121,s120,s147,s160]) ).
cnf(s163,plain,
spl0_17,
inference(rat,[],[s51,s27,s28,s29,s30,s31,s32,s160]) ).
cnf(s164,plain,
~ spl0_16,
inference(rat,[],[s162,s163]) ).
cnf(s165,plain,
spl0_15,
inference(rat,[],[s22,s164]) ).
cnf(s166,plain,
spl0_14,
inference(rat,[],[s21,s164]) ).
cnf(s167,plain,
spl0_13,
inference(rat,[],[s20,s164]) ).
cnf(s168,plain,
spl0_12,
inference(rat,[],[s19,s164]) ).
cnf(s169,plain,
spl0_11,
inference(rat,[],[s18,s164]) ).
cnf(s170,plain,
spl0_10,
inference(rat,[],[s17,s164]) ).
cnf(s176,plain,
$false,
inference(rat,[],[s51,s167,s168,s169,s170,s160,s165,s166]) ).
fof(f1777,plain,
$false,
inference(avatar_sat_refutation,[],[s176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP375-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n008.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:00:09 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/1.32 % (993462)Input is clausal, will run a generic CNF schedule.
% 3.30/1.32 % (993529)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3366333735:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.30/1.32 % (993530)lrs+10_1_sil=8000:sp=occurrence:random_seed=2217175514:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.30/1.32 % (993531)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=307449082:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.30/1.32 % (993528)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=932512378:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.30/1.32 % (993527)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=2452374581:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.30/1.32 % (993533)dis-21_1_sil=8000:lcm=predicate:random_seed=774637433:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.30/1.32 % (993532)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1812660142:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.30/1.32 % (993533)Refutation not found, incomplete strategy
% 3.30/1.32 % (993533)------------------------------
% 3.30/1.32 % (993533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.32 % (993533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.32 % (993533)CaDiCaL version: 2.1.3
% 3.30/1.32 % (993533)Termination reason: Refutation not found, incomplete strategy
% 3.30/1.32 % (993533)Time elapsed: 0.002 s
% 3.30/1.32 % (993533)Peak memory usage: 88 MB
% 3.30/1.32 % (993533)Instructions burned: 2 (million)
% 3.30/1.32 % (993530)Refutation not found, incomplete strategy
% 3.30/1.32 % (993530)------------------------------
% 3.30/1.32 % (993530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.32 % (993530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.32 % (993530)CaDiCaL version: 2.1.3
% 3.30/1.32 % (993530)Termination reason: Refutation not found, incomplete strategy
% 3.30/1.32 % (993530)Time elapsed: 0.004 s
% 3.30/1.32 % (993530)Peak memory usage: 88 MB
% 3.30/1.32 % (993530)Instructions burned: 5 (million)
% 3.30/1.32 % (993532)First to succeed.
% 3.30/1.32 % (993532)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-993462"
% 3.30/1.32 % (993531)Instruction limit reached!
% 3.30/1.32 % (993531)------------------------------
% 3.30/1.32 % (993531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.32 % (993531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.32 % (993531)CaDiCaL version: 2.1.3
% 3.30/1.32 % (993531)Termination reason: Instruction limit
% 3.30/1.32 % (993531)Termination phase: Saturation
% 3.30/1.32 % (993531)Time elapsed: 0.065 s
% 3.30/1.32 % (993531)Peak memory usage: 89 MB
% 3.30/1.32 % (993531)Instructions burned: 115 (million)
% 3.30/1.32 % (993541)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=578541401:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.30/1.32 % (993541)Refutation not found, incomplete strategy
% 3.30/1.32 % (993541)------------------------------
% 3.30/1.32 % (993541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.30/1.32 % (993541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.30/1.32 % (993541)CaDiCaL version: 2.1.3
% 3.30/1.32 % (993541)Termination reason: Refutation not found, incomplete strategy
% 3.30/1.32 % (993541)Time elapsed: 0.004 s
% 3.30/1.32 % (993541)Peak memory usage: 88 MB
% 3.30/1.32 % (993541)Instructions burned: 5 (million)
% 3.30/1.32 % (993530)------------------------------
% 3.30/1.32 % (993530)------------------------------
% 3.30/1.32 % (993533)------------------------------
% 3.30/1.32 % (993533)------------------------------
% 3.30/1.32 % (993532)Refutation found. Thanks to Tanya!
% 3.30/1.32 % SZS status Unsatisfiable for theBenchmark
% 3.30/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.51 % (993532)------------------------------
% 0.16/1.51 % (993532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.51 % (993532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.51 % (993532)CaDiCaL version: 2.1.3
% 0.16/1.51 % (993532)Termination reason: Refutation
% 0.16/1.51 % (993532)Time elapsed: 0.034 s
% 0.16/1.51 % (993532)Peak memory usage: 90 MB
% 0.16/1.51 % (993532)Instructions burned: 54 (million)
% 0.16/1.51 % (993532)------------------------------
% 0.16/1.51 % (993532)------------------------------
% 0.16/1.51 % (993462)Success in time 0.457 s
% 0.16/1.51 % Vampire exiting
%------------------------------------------------------------------------------