%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP377-1 : 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 : n016.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 2.85s 1.28s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 53
% Syntax : Number of formulae : 386 ( 17 unt; 21 def)
% Number of atoms : 1502 ( 430 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 2184 (1068 ~;1095 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 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(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(f16,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c10) = sk_c9
| sk_c10 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f20,plain,
( inverse(sk_c10) = sk_c9
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f19]) ).
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(f55,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c7,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f56,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = multiply(sk_c7,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f58,plain,
( sk_c10 = inverse(sk_c1)
| inverse(sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f60,plain,
( sk_c10 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f63,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c4,sk_c7) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| sk_c10 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| 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_c9) != sk_c10
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 != multiply(sk_c8,sk_c9)
| 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_c10 = multiply(sk_c8,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f98,plain,
( sk_c10 = multiply(sk_c8,sk_c9)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f99,plain,
( sk_c10 != multiply(sk_c8,sk_c9)
| 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(f111,definition,
( spl0_7
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f113,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f116,definition,
( spl0_8
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f118,plain,
( inverse(sk_c6) = sk_c5
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f121,definition,
( spl0_9
<=> sk_c10 = multiply(sk_c7,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f123,plain,
( sk_c10 = multiply(sk_c7,sk_c9)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f121]) ).
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(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(f160,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f60,f156,f111]) ).
fof(f161,plain,
( spl0_8
| spl0_16 ),
inference(avatar_split_clause,[],[f58,f156,f116]) ).
fof(f162,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f56,f156,f121]) ).
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(f184,plain,
( spl0_7
| spl0_5 ),
inference(avatar_split_clause,[],[f20,f101,f111]) ).
fof(f185,plain,
( spl0_8
| spl0_5 ),
inference(avatar_split_clause,[],[f18,f101,f116]) ).
fof(f186,plain,
( spl0_9
| spl0_5 ),
inference(avatar_split_clause,[],[f17,f101,f121]) ).
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(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(f196,plain,
( identity = multiply(sk_c5,sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f3,f118]) ).
fof(f197,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f3,f113]) ).
fof(f200,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f201,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c10,X0)) = multiply(sk_c9,X0)
| ~ spl0_15 ),
inference(superposition,[],[f4,f153]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c7,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f133]) ).
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(f232,plain,
( multiply(sk_c2,sk_c10) = multiply(sk_c9,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f201,f223]) ).
fof(f234,plain,
( sk_c9 = multiply(sk_c9,sk_c9)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f232,f153]) ).
fof(f273,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f206,f223]) ).
fof(f274,plain,
( sk_c3 = multiply(inverse(sk_c9),identity)
| ~ spl0_12 ),
inference(superposition,[],[f206,f194]) ).
fof(f278,plain,
( sk_c9 = multiply(inverse(sk_c3),sk_c8)
| ~ spl0_13 ),
inference(superposition,[],[f206,f143]) ).
fof(f281,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c10)
| ~ spl0_11 ),
inference(superposition,[],[f206,f133]) ).
fof(f285,plain,
( sk_c9 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_9 ),
inference(superposition,[],[f206,f123]) ).
fof(f287,plain,
( sk_c5 = multiply(inverse(sk_c7),identity)
| ~ spl0_7 ),
inference(superposition,[],[f206,f197]) ).
fof(f290,plain,
( sk_c6 = multiply(inverse(sk_c5),identity)
| ~ spl0_8 ),
inference(superposition,[],[f206,f196]) ).
fof(f293,plain,
( sk_c6 = multiply(sk_c7,identity)
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_demodulation,[],[f290,f113]) ).
fof(f298,plain,
( sk_c7 = multiply(sk_c7,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f281,f128]) ).
fof(f301,plain,
( sk_c9 = multiply(sk_c9,sk_c8)
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f278,f138]) ).
fof(f305,plain,
( identity = sk_c9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f273,f3]) ).
fof(f307,plain,
( multiply(sk_c7,sk_c9) = sk_c6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f293,f305]) ).
fof(f308,plain,
( sk_c10 = sk_c6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f307,f123]) ).
fof(f312,plain,
( inverse(sk_c10) = sk_c5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f118,f308]) ).
fof(f318,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f203,f298]) ).
fof(f319,plain,
( sk_c10 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f206,f298]) ).
fof(f321,plain,
( identity = sk_c10
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f319,f3]) ).
fof(f322,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f318,f133]) ).
fof(f324,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f321,f305]) ).
fof(f329,plain,
( sk_c8 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f206,f301]) ).
fof(f331,plain,
( identity = sk_c8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f329,f3]) ).
fof(f334,plain,
( sk_c9 = sk_c8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f331,f305]) ).
fof(f337,plain,
( sk_c10 != multiply(sk_c9,sk_c9)
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f99,f334]) ).
fof(f338,plain,
( sk_c10 != sk_c9
| spl0_4
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f337,f234]) ).
fof(f340,plain,
( sk_c3 = multiply(inverse(sk_c9),sk_c9)
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f274,f305]) ).
fof(f341,plain,
( identity = sk_c3
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f340,f3]) ).
fof(f342,plain,
( sk_c9 = sk_c3
| ~ spl0_12
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f341,f305]) ).
fof(f352,plain,
( $false
| spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f324,f338]) ).
fof(f353,plain,
( spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f352]) ).
fof(f398,plain,
( sk_c9 != sk_c5
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f103,f312]) ).
fof(f402,plain,
( sk_c10 != sk_c5
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f398,f324]) ).
fof(f452,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c9)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f287,f305]) ).
fof(f453,plain,
( sk_c5 = multiply(inverse(sk_c7),sk_c10)
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f452,f324]) ).
fof(f454,plain,
( sk_c9 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f453,f285]) ).
fof(f455,plain,
( sk_c10 = sk_c5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f454,f324]) ).
fof(f456,plain,
( $false
| spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f455,f402]) ).
fof(f457,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f456]) ).
fof(f458,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,f324]) ).
fof(f459,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f102,f324]) ).
fof(f478,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,[],[f458,f148]) ).
fof(f483,plain,
( ! [X0] :
( identity != sk_c10
| sk_c10 != multiply(sk_c10,inverse(sk_c10))
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f458,f3]) ).
fof(f487,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,inverse(sk_c10))
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f483,f321]) ).
fof(f569,plain,
( ! [X0] :
( sk_c10 != sk_c9
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f478,f153]) ).
fof(f571,definition,
( spl0_22
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f572,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f574,definition,
( spl0_23
<=> sk_c10 = multiply(sk_c10,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f575,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f578,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c5)
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f487,f312]) ).
fof(f586,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f569,f324]) ).
fof(f587,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,inverse(sk_c10))
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f578,f455]) ).
fof(f595,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f586,f151,f146,f131,f126,f88,f574,f571]) ).
fof(f596,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c5)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f587,f312]) ).
fof(f602,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(sk_c10) != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f596,f455]) ).
fof(f606,plain,
( ! [X0] :
( sk_c5 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f602,f312]) ).
fof(f609,plain,
( ! [X0] :
( sk_c10 != inverse(inverse(X0))
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f606,f455]) ).
fof(f611,plain,
( ~ spl0_23
| spl0_22
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f609,f151,f146,f131,f126,f121,f116,f111,f88,f571,f574]) ).
fof(f663,plain,
( multiply(sk_c2,sk_c10) = multiply(sk_c9,sk_c10)
| ~ spl0_15
| ~ spl0_23 ),
inference(superposition,[],[f201,f575]) ).
fof(f664,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_23 ),
inference(superposition,[],[f206,f575]) ).
fof(f665,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c10,X0))
| ~ spl0_23 ),
inference(superposition,[],[f4,f575]) ).
fof(f666,plain,
( identity = sk_c10
| ~ spl0_23 ),
inference(forward_demodulation,[],[f664,f3]) ).
fof(f667,plain,
( multiply(sk_c2,sk_c10) = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f663,f324]) ).
fof(f668,plain,
( sk_c10 = multiply(sk_c2,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f667,f575]) ).
fof(f684,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(superposition,[],[f572,f459]) ).
fof(f691,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_16
| ~ spl0_22 ),
inference(superposition,[],[f572,f158]) ).
fof(f699,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f684,f459]) ).
fof(f708,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f699,f575]) ).
fof(f709,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f730,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,f324]) ).
fof(f731,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f730,f324]) ).
fof(f735,plain,
( sk_c10 != sk_c10
| sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f731,f459]) ).
fof(f745,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f735]) ).
fof(f753,plain,
( sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f745,f575]) ).
fof(f782,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c10,X0))
| ~ spl0_23 ),
inference(superposition,[],[f206,f665]) ).
fof(f785,plain,
( ! [X0] : multiply(sk_c10,X0) = X0
| ~ spl0_23 ),
inference(forward_demodulation,[],[f782,f206]) ).
fof(f939,plain,
( sk_c8 = multiply(sk_c3,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f143,f324]) ).
fof(f954,plain,
( sk_c8 = multiply(sk_c9,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f939,f342]) ).
fof(f959,plain,
( sk_c8 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f954,f324]) ).
fof(f961,plain,
( sk_c10 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_demodulation,[],[f959,f575]) ).
fof(f970,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f753,f961]) ).
fof(f971,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f970]) ).
fof(f972,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,f324]) ).
fof(f975,plain,
( sk_c10 != sk_c10
| sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f972,f148]) ).
fof(f980,plain,
( sk_c10 != multiply(sk_c2,sk_c10)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f975]) ).
fof(f986,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f980,f668]) ).
fof(f987,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f986]) ).
fof(f1059,plain,
( identity = multiply(sk_c10,sk_c1)
| ~ spl0_16 ),
inference(superposition,[],[f3,f158]) ).
fof(f1060,plain,
( identity = sk_c1
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1059,f785]) ).
fof(f1062,plain,
( sk_c10 = sk_c1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1060,f321]) ).
fof(f1088,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f172,f1062]) ).
fof(f1089,plain,
( sk_c10 = sk_c9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1088,f575]) ).
fof(f1180,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f102,f1089]) ).
fof(f1190,plain,
( sk_c10 = multiply(sk_c8,sk_c10)
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f98,f1089]) ).
fof(f1193,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c8,multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f4,f1190]) ).
fof(f1194,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1193,f785]) ).
fof(f1196,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f92,f1089]) ).
fof(f1197,plain,
( ! [X2] :
( sk_c10 != inverse(X2)
| sk_c8 != multiply(X2,sk_c10) )
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1196,f1089]) ).
fof(f1208,plain,
( sk_c10 != sk_c10
| sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f1197,f1180]) ).
fof(f1215,plain,
( sk_c8 != multiply(sk_c10,sk_c10)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f1208]) ).
fof(f1219,plain,
( sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1215,f575]) ).
fof(f1238,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f206,f1194]) ).
fof(f1295,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f1238,f3]) ).
fof(f1302,plain,
( sk_c10 = sk_c8
| ~ spl0_4
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1295,f321]) ).
fof(f1305,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1302,f1219]) ).
fof(f1306,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1305]) ).
fof(f1307,plain,
( spl0_23
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f322,f131,f126,f574]) ).
fof(f1371,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f691,f1180]) ).
fof(f1373,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1371,f1062]) ).
fof(f1375,plain,
( ~ spl0_23
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1373,f574,f571,f170,f156,f131,f126,f101,f574]) ).
fof(f1395,plain,
( identity = multiply(sk_c9,sk_c10)
| ~ spl0_5 ),
inference(superposition,[],[f3,f102]) ).
fof(f1397,plain,
( sk_c10 = sk_c1
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f666,f1060]) ).
fof(f1402,plain,
( sk_c10 = inverse(sk_c10)
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f158,f1397]) ).
fof(f1403,plain,
( sk_c9 = multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f172,f1397]) ).
fof(f1404,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f1402,f102]) ).
fof(f1418,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_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f89,f1404]) ).
fof(f1419,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f1418,f1402]) ).
fof(f1427,plain,
( ! [X0] :
( sk_c10 != multiply(sk_c10,sk_c10)
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(duplicate_literal_removal,[],[f1419]) ).
fof(f1453,plain,
( ! [X0] :
( sk_c10 != sk_c9
| inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1427,f1403]) ).
fof(f1458,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1453,f1404]) ).
fof(f1463,plain,
( spl0_22
| ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1458,f574,f170,f156,f101,f88,f571]) ).
fof(f1501,plain,
( sk_c10 != multiply(sk_c1,sk_c10)
| ~ spl0_16
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f691,f1402]) ).
fof(f1503,plain,
( sk_c10 != multiply(sk_c10,sk_c10)
| ~ spl0_16
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1501,f1397]) ).
fof(f1505,plain,
( sk_c10 != sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1503,f1403]) ).
fof(f1507,plain,
( $false
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1505,f1404]) ).
fof(f1508,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1507]) ).
fof(f1509,plain,
( ! [X1] :
( sk_c10 != multiply(X1,sk_c10)
| sk_c10 != inverse(X1) )
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f95,f1404]) ).
fof(f1510,plain,
( sk_c10 = sk_c9
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f575,f1403]) ).
fof(f1520,plain,
( identity != sk_c10
| sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f1509,f3]) ).
fof(f1530,plain,
( sk_c10 != inverse(inverse(sk_c10))
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1520,f666]) ).
fof(f1535,plain,
( sk_c10 != inverse(sk_c9)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1530,f102]) ).
fof(f1538,plain,
( sk_c10 != inverse(sk_c10)
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1535,f1404]) ).
fof(f1539,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f1538,f1402]) ).
fof(f1540,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f1539]) ).
fof(f1541,plain,
( sk_c10 = multiply(inverse(sk_c1),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f206,f172]) ).
fof(f1543,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1541,f158]) ).
fof(f1549,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(f1563,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,[],[f1549,f172]) ).
fof(f1583,definition,
( spl0_44
<=> sk_c10 = multiply(sk_c10,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_44])],[avatar_definition]) ).
fof(f1584,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1583]) ).
fof(f1588,definition,
( spl0_45
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_45])],[avatar_definition]) ).
fof(f1589,plain,
( sk_c10 = sk_c9
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f1588]) ).
fof(f1591,plain,
( spl0_22
| ~ spl0_44
| ~ spl0_45
| ~ spl0_1
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1563,f170,f156,f88,f1588,f1583,f571]) ).
fof(f1616,plain,
( spl0_44
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1543,f170,f156,f1583]) ).
fof(f1618,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_44 ),
inference(superposition,[],[f206,f1584]) ).
fof(f1619,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c9,X0))
| ~ spl0_44 ),
inference(superposition,[],[f4,f1584]) ).
fof(f1620,plain,
( identity = sk_c9
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1618,f3]) ).
fof(f1634,plain,
( multiply(sk_c10,sk_c10) = multiply(sk_c10,identity)
| ~ spl0_5
| ~ spl0_44 ),
inference(superposition,[],[f1619,f1395]) ).
fof(f1643,plain,
( multiply(sk_c10,sk_c9) = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1634,f1620]) ).
fof(f1646,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_5
| ~ spl0_44 ),
inference(forward_demodulation,[],[f1643,f1584]) ).
fof(f1660,plain,
( spl0_23
| ~ spl0_5
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f1646,f1583,f101,f574]) ).
fof(f1661,plain,
( spl0_45
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1404,f574,f156,f101,f1588]) ).
fof(f1662,plain,
( spl0_45
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f1510,f574,f170,f156,f1588]) ).
fof(f1664,plain,
( sk_c10 = multiply(sk_c8,sk_c10)
| ~ spl0_4
| ~ spl0_45 ),
inference(superposition,[],[f98,f1589]) ).
fof(f1688,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c9 != inverse(X2) )
| ~ spl0_2
| ~ spl0_45 ),
inference(forward_demodulation,[],[f92,f1589]) ).
fof(f1689,plain,
( ! [X2] :
( sk_c8 != multiply(X2,sk_c10)
| sk_c10 != inverse(X2) )
| ~ spl0_2
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1688,f1589]) ).
fof(f1691,plain,
( sk_c10 != sk_c8
| sk_c10 != inverse(identity)
| ~ spl0_2
| ~ spl0_45 ),
inference(superposition,[],[f1689,f1]) ).
fof(f1701,plain,
( sk_c10 != inverse(sk_c9)
| sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1691,f1620]) ).
fof(f1704,definition,
( spl0_46
<=> sk_c10 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_46])],[avatar_definition]) ).
fof(f1706,plain,
( sk_c10 != sk_c8
| spl0_46 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f1710,plain,
( sk_c10 != inverse(sk_c10)
| sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1701,f1589]) ).
fof(f1714,plain,
( sk_c10 != sk_c9
| sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1710,f102]) ).
fof(f1717,plain,
( sk_c10 != sk_c8
| ~ spl0_2
| ~ spl0_5
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[],[f1714,f1589]) ).
fof(f1720,plain,
( ~ spl0_46
| ~ spl0_2
| ~ spl0_5
| ~ spl0_44
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f1717,f1588,f1583,f101,f91,f1704]) ).
fof(f1748,plain,
( sk_c10 = multiply(inverse(sk_c8),sk_c10)
| ~ spl0_4
| ~ spl0_45 ),
inference(superposition,[],[f206,f1664]) ).
fof(f1887,plain,
( ! [X0] : multiply(sk_c10,X0) = multiply(inverse(sk_c8),multiply(sk_c10,X0))
| ~ spl0_4
| ~ spl0_45 ),
inference(superposition,[],[f4,f1748]) ).
fof(f1888,plain,
( ! [X0] : multiply(inverse(sk_c8),X0) = X0
| ~ spl0_4
| ~ spl0_23
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1887,f785]) ).
fof(f1964,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_23
| ~ spl0_45 ),
inference(superposition,[],[f1888,f3]) ).
fof(f1975,plain,
( sk_c9 = sk_c8
| ~ spl0_4
| ~ spl0_23
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1964,f1620]) ).
fof(f1977,plain,
( sk_c10 = sk_c8
| ~ spl0_4
| ~ spl0_23
| ~ spl0_44
| ~ spl0_45 ),
inference(forward_demodulation,[],[f1975,f1589]) ).
fof(f1980,plain,
( $false
| ~ spl0_4
| ~ spl0_23
| ~ spl0_44
| ~ spl0_45
| spl0_46 ),
inference(forward_subsumption_resolution,[],[f1977,f1706]) ).
fof(f1981,plain,
( ~ spl0_4
| ~ spl0_23
| ~ spl0_44
| ~ spl0_45
| spl0_46 ),
inference(avatar_contradiction_clause,[],[f1980]) ).
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(s14,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f160]) ).
cnf(s15,plain,
( spl0_8
| spl0_16 ),
inference(sat_conversion,[],[f161]) ).
cnf(s16,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f162]) ).
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(s34,plain,
( spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f184]) ).
cnf(s35,plain,
( spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f185]) ).
cnf(s36,plain,
( spl0_5
| spl0_9 ),
inference(sat_conversion,[],[f186]) ).
cnf(s37,plain,
( spl0_5
| spl0_10 ),
inference(sat_conversion,[],[f187]) ).
cnf(s38,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f188]) ).
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,[],[f353]) ).
cnf(s44,plain,
( spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f457]) ).
cnf(s53,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f595]) ).
cnf(s58,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f611]) ).
cnf(s70,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f709]) ).
cnf(s80,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(sat_conversion,[],[f971]) ).
cnf(s81,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_15
| ~ spl0_23 ),
inference(sat_conversion,[],[f987]) ).
cnf(s93,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_23 ),
inference(sat_conversion,[],[f1306]) ).
cnf(s94,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_23 ),
inference(sat_conversion,[],[f1307]) ).
cnf(s103,plain,
( ~ spl0_23
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_5
| ~ spl0_23 ),
inference(sat_conversion,[],[f1375]) ).
cnf(s104,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(rat,[],[s103]) ).
cnf(s111,plain,
( ~ spl0_1
| ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f1463]) ).
cnf(s119,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_17
| ~ spl0_22
| ~ spl0_23 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s124,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_16
| ~ spl0_23 ),
inference(sat_conversion,[],[f1540]) ).
cnf(s130,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_17
| spl0_22
| ~ spl0_44
| ~ spl0_45 ),
inference(sat_conversion,[],[f1591]) ).
cnf(s132,plain,
( ~ spl0_16
| ~ spl0_17
| spl0_44 ),
inference(sat_conversion,[],[f1616]) ).
cnf(s139,plain,
( ~ spl0_5
| spl0_23
| ~ spl0_44 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s140,plain,
( ~ spl0_5
| ~ spl0_16
| ~ spl0_23
| spl0_45 ),
inference(sat_conversion,[],[f1661]) ).
cnf(s141,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_23
| spl0_45 ),
inference(sat_conversion,[],[f1662]) ).
cnf(s149,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_44
| ~ spl0_45
| ~ spl0_46 ),
inference(sat_conversion,[],[f1720]) ).
cnf(s160,plain,
( ~ spl0_4
| ~ spl0_23
| ~ spl0_44
| ~ spl0_45
| spl0_46 ),
inference(sat_conversion,[],[f1981]) ).
cnf(s161,plain,
spl0_4,
inference(rat,[],[s43,s7,s8,s9,s10,s11,s12]) ).
cnf(s162,plain,
spl0_5,
inference(rat,[],[s44,s34,s35,s36,s37,s38,s41,s42]) ).
cnf(s163,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_3 ),
inference(rat,[],[s81,s21,s22,s124,s94,s162]) ).
cnf(s164,plain,
( spl0_11
| ~ spl0_3 ),
inference(rat,[],[s139,s124,s132,s18,s28,s162]) ).
cnf(s165,plain,
( ~ spl0_11
| ~ spl0_3 ),
inference(rat,[],[s139,s124,s132,s17,s27,s163,s162]) ).
cnf(s166,plain,
~ spl0_3,
inference(rat,[],[s165,s164]) ).
cnf(s167,plain,
( spl0_16
| ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s80,s19,s20,s21,s22,s94,s162]) ).
cnf(s168,plain,
( ~ spl0_16
| ~ spl0_23
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s80,s29,s30,s31,s32,s93,s161,s162]) ).
cnf(s169,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_2 ),
inference(rat,[],[s168,s167,s94]) ).
cnf(s170,plain,
( spl0_11
| ~ spl0_2 ),
inference(rat,[],[s149,s160,s141,s139,s132,s18,s28,s162,s161]) ).
cnf(s171,plain,
( ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s149,s160,s141,s139,s132,s17,s27,s169,s161,s162]) ).
cnf(s172,plain,
~ spl0_2,
inference(rat,[],[s171,s170]) ).
cnf(s173,plain,
spl0_1,
inference(rat,[],[s2,s161,s162,s166,s172]) ).
cnf(s174,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_23
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_15 ),
inference(rat,[],[s70,s58,s173,s162]) ).
cnf(s175,plain,
( spl0_16
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s174,s14,s15,s16,s21,s22,s94]) ).
cnf(s176,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_23
| ~ spl0_10
| ~ spl0_11 ),
inference(rat,[],[s53,s70,s162,s173]) ).
cnf(s177,plain,
( ~ spl0_17
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s104,s130,s132,s140,s175,s94,s162,s173]) ).
cnf(s178,plain,
( ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s176,s31,s32,s177,s94]) ).
cnf(s179,plain,
( ~ spl0_23
| ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s119,s111,s173,s162]) ).
cnf(s180,plain,
( ~ spl0_17
| ~ spl0_16 ),
inference(rat,[],[s179,s139,s132,s162]) ).
cnf(s181,plain,
spl0_11,
inference(rat,[],[s180,s18,s28]) ).
cnf(s182,plain,
~ spl0_10,
inference(rat,[],[s178,s181]) ).
cnf(s183,plain,
spl0_17,
inference(rat,[],[s27,s182]) ).
cnf(s184,plain,
spl0_16,
inference(rat,[],[s17,s182]) ).
cnf(s185,plain,
$false,
inference(rat,[],[s180,s184,s183]) ).
fof(f1982,plain,
$false,
inference(avatar_sat_refutation,[],[s185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP377-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:04:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.85/1.28 % (2386662)Input is clausal, will run a generic CNF schedule.
% 2.85/1.28 % (2386667)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=2336187676:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.85/1.28 % (2386670)lrs+10_1_sil=8000:sp=occurrence:random_seed=1672471101:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.85/1.28 % (2386672)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2161864080:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.85/1.28 % (2386669)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3955704830:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.85/1.28 % (2386671)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1838350869:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.85/1.28 % (2386668)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4071625036:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.85/1.28 % (2386670)Refutation not found, incomplete strategy
% 2.85/1.28 % (2386670)------------------------------
% 2.85/1.28 % (2386670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2386670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2386670)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2386670)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2386670)Time elapsed: 0.004 s
% 2.85/1.28 % (2386670)Peak memory usage: 88 MB
% 2.85/1.28 % (2386670)Instructions burned: 5 (million)
% 2.85/1.28 % (2386673)dis-21_1_sil=8000:lcm=predicate:random_seed=2007116661: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)
% 2.85/1.28 % (2386673)Refutation not found, incomplete strategy
% 2.85/1.28 % (2386673)------------------------------
% 2.85/1.28 % (2386673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2386673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2386673)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2386673)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2386673)Time elapsed: 0.002 s
% 2.85/1.28 % (2386673)Peak memory usage: 88 MB
% 2.85/1.28 % (2386673)Instructions burned: 2 (million)
% 2.85/1.28 % (2386672)First to succeed.
% 2.85/1.28 % (2386672)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2386662"
% 2.85/1.28 % (2386671)Instruction limit reached!
% 2.85/1.28 % (2386671)------------------------------
% 2.85/1.28 % (2386671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2386671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2386671)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2386671)Termination reason: Instruction limit
% 2.85/1.28 % (2386671)Termination phase: Saturation
% 2.85/1.28 % (2386671)Time elapsed: 0.065 s
% 2.85/1.28 % (2386671)Peak memory usage: 89 MB
% 2.85/1.28 % (2386671)Instructions burned: 116 (million)
% 2.85/1.28 % (2386681)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=3427159613:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.85/1.28 % (2386681)Refutation not found, incomplete strategy
% 2.85/1.28 % (2386681)------------------------------
% 2.85/1.28 % (2386681)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.85/1.28 % (2386681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/1.28 % (2386681)CaDiCaL version: 2.1.3
% 2.85/1.28 % (2386681)Termination reason: Refutation not found, incomplete strategy
% 2.85/1.28 % (2386681)Time elapsed: 0.004 s
% 2.85/1.28 % (2386681)Peak memory usage: 88 MB
% 2.85/1.28 % (2386681)Instructions burned: 5 (million)
% 2.85/1.28 % (2386670)------------------------------
% 2.85/1.28 % (2386670)------------------------------
% 2.85/1.28 % (2386673)------------------------------
% 2.85/1.28 % (2386673)------------------------------
% 2.85/1.28 % (2386672)Refutation found. Thanks to Tanya!
% 2.85/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.85/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.38 % (2386672)------------------------------
% 3.61/1.38 % (2386672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.38 % (2386672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.38 % (2386672)CaDiCaL version: 2.1.3
% 3.61/1.38 % (2386672)Termination reason: Refutation
% 3.61/1.38 % (2386672)Time elapsed: 0.042 s
% 3.61/1.38 % (2386672)Peak memory usage: 90 MB
% 3.61/1.38 % (2386672)Instructions burned: 62 (million)
% 3.61/1.38 % (2386672)------------------------------
% 3.61/1.38 % (2386672)------------------------------
% 3.61/1.38 % (2386662)Success in time 0.449 s
% 3.61/1.38 % Vampire exiting
%------------------------------------------------------------------------------