%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 10:17:18 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 47
% Syntax : Number of formulae : 404 ( 20 unt; 21 def)
% Number of atoms : 1455 ( 344 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2079 (1028 ~;1030 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c1)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c7 = inverse(sk_c2)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c6 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f44]) ).
fof(f54,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f54]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| inverse(X2) != sk_c6
| multiply(X2,sk_c8) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c8)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f64]) ).
fof(f67,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f68,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f71,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f73,definition,
( spl0_3
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f74,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_4
<=> ! [X2] :
( sk_c6 != inverse(X2)
| sk_c6 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( ! [X2] :
( sk_c6 != multiply(X2,sk_c8)
| sk_c6 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,definition,
( spl0_5
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f81,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl0_6
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f84,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f85,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f65,f83,f80,f77,f73,f70,f67]) ).
fof(f87,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f88,plain,
( sk_c7 != multiply(sk_c5,sk_c6)
| spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f89,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl0_8
<=> sk_c6 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f93,plain,
( sk_c6 = multiply(sk_c3,sk_c8)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f96,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f98,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f101,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f103,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f106,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f108,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f110,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f55,f91,f73]) ).
fof(f112,definition,
( spl0_12
<=> sk_c6 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f114,plain,
( sk_c6 = inverse(sk_c3)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f119,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f45,f112,f73]) ).
fof(f121,definition,
( spl0_13
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f123,plain,
( sk_c7 = inverse(sk_c2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f124,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f43,f121,f87]) ).
fof(f125,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f41,f121,f96]) ).
fof(f126,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f39,f121,f101]) ).
fof(f127,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f37,f121,f106]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f35,f121,f73]) ).
fof(f130,definition,
( spl0_14
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f131,plain,
( sk_c6 != multiply(sk_c2,sk_c7)
| spl0_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f132,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f130,f87]) ).
fof(f134,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f130,f96]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f29,f130,f101]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f27,f130,f106]) ).
fof(f137,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f25,f130,f73]) ).
fof(f139,definition,
( spl0_15
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f141,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f139,f87]) ).
fof(f143,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f139,f96]) ).
fof(f144,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f139,f101]) ).
fof(f145,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f139,f106]) ).
fof(f146,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f15,f139,f73]) ).
fof(f148,definition,
( spl0_16
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f150,plain,
( multiply(sk_c1,sk_c8) = sk_c7
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f151,plain,
( spl0_7
| spl0_16 ),
inference(avatar_split_clause,[],[f13,f148,f87]) ).
fof(f152,plain,
( spl0_9
| spl0_16 ),
inference(avatar_split_clause,[],[f11,f148,f96]) ).
fof(f153,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f9,f148,f101]) ).
fof(f154,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f7,f148,f106]) ).
fof(f155,plain,
( spl0_3
| spl0_16 ),
inference(avatar_split_clause,[],[f5,f148,f73]) ).
fof(f156,plain,
( sk_c8 != sk_c8
| sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f71,f103]) ).
fof(f157,plain,
( sk_c8 != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f156]) ).
fof(f158,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f157,f108]) ).
fof(f159,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f158]) ).
fof(f160,plain,
( sk_c8 != sk_c6
| sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f71,f132]) ).
fof(f161,plain,
( sk_c8 != sk_c7
| sk_c8 != sk_c6
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f160,f123]) ).
fof(f163,definition,
( spl0_17
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f164,plain,
( sk_c8 = sk_c6
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f165,plain,
( sk_c8 != sk_c6
| spl0_17 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f167,definition,
( spl0_18
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f168,plain,
( sk_c8 = sk_c7
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( sk_c8 != sk_c7
| spl0_18 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f170,plain,
( ~ spl0_17
| ~ spl0_18
| ~ spl0_2
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f161,f130,f121,f70,f167,f163]) ).
fof(f177,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_15 ),
inference(superposition,[],[f3,f141]) ).
fof(f179,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f98]) ).
fof(f180,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_13 ),
inference(superposition,[],[f3,f123]) ).
fof(f182,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c7))
| ~ spl0_2 ),
inference(superposition,[],[f71,f3]) ).
fof(f184,definition,
( spl0_20
<=> sk_c8 = inverse(inverse(sk_c7)) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f186,plain,
( sk_c8 != inverse(inverse(sk_c7))
| spl0_20 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f188,definition,
( spl0_21
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f189,plain,
( identity = sk_c8
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( identity != sk_c8
| spl0_21 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f191,plain,
( ~ spl0_20
| ~ spl0_21
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f182,f70,f188,f184]) ).
fof(f194,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f201,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f194,f1]) ).
fof(f204,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f177]) ).
fof(f205,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c1,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f204,f1]) ).
fof(f214,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f205,f150]) ).
fof(f304,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f201,f214]) ).
fof(f313,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f201,f89]) ).
fof(f315,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_14 ),
inference(superposition,[],[f201,f132]) ).
fof(f317,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c6)
| ~ spl0_8 ),
inference(superposition,[],[f201,f93]) ).
fof(f323,plain,
( sk_c8 = multiply(sk_c6,sk_c6)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f114]) ).
fof(f325,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f315,f123]) ).
fof(f327,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f313,f98]) ).
fof(f330,plain,
( identity = sk_c7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f304,f3]) ).
fof(f341,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f74,f330]) ).
fof(f344,plain,
( identity != sk_c8
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(superposition,[],[f169,f330]) ).
fof(f345,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f179,f330]) ).
fof(f358,plain,
( identity = sk_c5
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f345,f1]) ).
fof(f360,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f341,f1]) ).
fof(f365,plain,
( $false
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f360,f165]) ).
fof(f366,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f375,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f360,f148,f139,f73,f163]) ).
fof(f406,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f325,f164]) ).
fof(f407,plain,
( identity = multiply(identity,sk_c8)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f406,f330]) ).
fof(f408,plain,
( identity = sk_c8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f407,f1]) ).
fof(f411,plain,
( sk_c6 != multiply(identity,sk_c8)
| spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f75,f330]) ).
fof(f412,plain,
( identity != multiply(sk_c5,sk_c6)
| spl0_7
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f88,f330]) ).
fof(f413,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f325,f330]) ).
fof(f418,plain,
( sk_c8 != sk_c6
| spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f411,f1]) ).
fof(f419,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f413,f1]) ).
fof(f423,plain,
( ~ spl0_17
| spl0_3
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f418,f148,f139,f73,f163]) ).
fof(f435,plain,
( identity != sk_c8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(superposition,[],[f165,f419]) ).
fof(f438,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f323,f419]) ).
fof(f439,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f438,f1]) ).
fof(f443,plain,
( ~ spl0_21
| ~ spl0_15
| ~ spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f344,f167,f148,f139,f188]) ).
fof(f444,plain,
( ~ spl0_21
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f435,f163,f148,f139,f130,f121,f188]) ).
fof(f445,plain,
( spl0_21
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f439,f148,f139,f130,f121,f112,f91,f188]) ).
fof(f449,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f360,f419]) ).
fof(f450,plain,
( ! [X2] :
( identity != inverse(X2)
| sk_c6 != multiply(X2,sk_c8) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f78,f419]) ).
fof(f452,plain,
( spl0_21
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f408,f163,f148,f139,f130,f121,f188]) ).
fof(f458,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f449,f148,f139,f130,f121,f73,f188]) ).
fof(f459,plain,
( ! [X2] :
( identity != multiply(X2,sk_c8)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f450,f419]) ).
fof(f465,plain,
( identity = multiply(identity,sk_c1)
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f177,f189]) ).
fof(f474,plain,
( identity = sk_c1
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f465,f1]) ).
fof(f486,plain,
( sk_c8 = inverse(identity)
| ~ spl0_15
| ~ spl0_21 ),
inference(superposition,[],[f141,f474]) ).
fof(f487,plain,
( identity = inverse(identity)
| ~ spl0_15
| ~ spl0_21 ),
inference(forward_demodulation,[],[f486,f189]) ).
fof(f517,plain,
( identity != multiply(identity,sk_c6)
| spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f412,f358]) ).
fof(f522,plain,
( identity != sk_c6
| spl0_7
| ~ spl0_9
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f517,f1]) ).
fof(f525,plain,
( $false
| spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f522,f419]) ).
fof(f526,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f525]) ).
fof(f531,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f459,f189]) ).
fof(f534,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f531,f3]) ).
fof(f535,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f534]) ).
fof(f537,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f535,f487]) ).
fof(f540,plain,
( $false
| ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f537,f487]) ).
fof(f541,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f540]) ).
fof(f555,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f68,f330]) ).
fof(f556,plain,
( ! [X4] :
( sk_c7 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f555,f419]) ).
fof(f557,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f556,f330]) ).
fof(f561,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f557,f3]) ).
fof(f562,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f561]) ).
fof(f564,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f562,f487]) ).
fof(f567,plain,
( $false
| ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f564,f487]) ).
fof(f568,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f569,plain,
( ! [X0] :
( sk_c7 != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_6
| ~ spl0_21 ),
inference(forward_demodulation,[],[f84,f189]) ).
fof(f570,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f569,f330]) ).
fof(f571,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f570,f189]) ).
fof(f580,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f571,f3]) ).
fof(f581,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f580]) ).
fof(f583,plain,
( identity != inverse(identity)
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f581,f487]) ).
fof(f586,plain,
( $false
| ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f583,f487]) ).
fof(f587,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f588,plain,
( ! [X2] :
( sk_c6 != multiply(X2,identity)
| sk_c6 != inverse(X2) )
| ~ spl0_4
| ~ spl0_21 ),
inference(forward_demodulation,[],[f78,f189]) ).
fof(f602,plain,
( identity = inverse(sk_c4)
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f108,f189]) ).
fof(f607,plain,
( identity = sk_c6
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f164,f189]) ).
fof(f624,plain,
( identity = sk_c7
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f168,f189]) ).
fof(f625,plain,
( identity = multiply(sk_c4,sk_c7)
| ~ spl0_10
| ~ spl0_21 ),
inference(forward_demodulation,[],[f103,f189]) ).
fof(f630,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f98]) ).
fof(f631,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f180,f624]) ).
fof(f632,plain,
( sk_c8 != inverse(inverse(identity))
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(superposition,[],[f186,f624]) ).
fof(f633,plain,
( identity != inverse(inverse(identity))
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f632,f189]) ).
fof(f634,plain,
( identity = sk_c2
| ~ spl0_13
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f631,f1]) ).
fof(f636,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f3,f602]) ).
fof(f637,plain,
( identity = sk_c4
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f636,f1]) ).
fof(f639,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f602,f637]) ).
fof(f650,plain,
( sk_c7 = multiply(sk_c5,identity)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f89,f607]) ).
fof(f651,plain,
( identity = multiply(sk_c5,identity)
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f650,f624]) ).
fof(f656,plain,
( sk_c6 != multiply(sk_c2,identity)
| spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f131,f624]) ).
fof(f657,plain,
( sk_c6 != multiply(identity,identity)
| ~ spl0_13
| spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f656,f634]) ).
fof(f658,plain,
( identity != sk_c6
| ~ spl0_13
| spl0_14
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f657,f1]) ).
fof(f659,plain,
( $false
| ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f658,f607]) ).
fof(f660,plain,
( ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f667,plain,
( identity = multiply(identity,sk_c7)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f625,f637]) ).
fof(f668,plain,
( identity = sk_c7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f667,f1]) ).
fof(f675,plain,
( identity != inverse(identity)
| ~ spl0_11
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f633,f639]) ).
fof(f676,plain,
( $false
| ~ spl0_11
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f675,f639]) ).
fof(f677,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f694,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c6 != inverse(X2) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f588,f607]) ).
fof(f695,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_21 ),
inference(forward_demodulation,[],[f694,f607]) ).
fof(f701,plain,
( identity != identity
| identity != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(superposition,[],[f695,f651]) ).
fof(f702,plain,
( identity != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f701]) ).
fof(f705,plain,
( identity != sk_c7
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_demodulation,[],[f702,f98]) ).
fof(f709,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f705,f668]) ).
fof(f710,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f709]) ).
fof(f735,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| inverse(X0) != sk_c8 )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f569,f668]) ).
fof(f737,plain,
( ! [X0] :
( identity != multiply(X0,identity)
| identity != inverse(X0) )
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f735,f189]) ).
fof(f743,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f737,f3]) ).
fof(f746,plain,
( identity != inverse(inverse(identity))
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f743]) ).
fof(f749,plain,
( identity != inverse(identity)
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_demodulation,[],[f746,f639]) ).
fof(f754,plain,
( $false
| ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f749,f639]) ).
fof(f755,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f796,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_3 ),
inference(superposition,[],[f201,f74]) ).
fof(f798,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f74,f168]) ).
fof(f801,plain,
( sk_c8 = multiply(sk_c4,sk_c8)
| ~ spl0_10
| ~ spl0_18 ),
inference(forward_demodulation,[],[f103,f168]) ).
fof(f815,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f81,f168]) ).
fof(f816,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c8 != inverse(X1) )
| ~ spl0_5
| ~ spl0_18 ),
inference(forward_demodulation,[],[f815,f168]) ).
fof(f822,plain,
( sk_c8 != sk_c6
| sk_c8 != inverse(sk_c4)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_18 ),
inference(superposition,[],[f816,f801]) ).
fof(f836,definition,
( spl0_26
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f837,plain,
( identity = sk_c6
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f842,plain,
( sk_c6 = multiply(inverse(sk_c5),sk_c7)
| ~ spl0_7 ),
inference(superposition,[],[f201,f89]) ).
fof(f843,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f89]) ).
fof(f844,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f842,f98]) ).
fof(f845,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c8)
| ~ spl0_10 ),
inference(superposition,[],[f201,f103]) ).
fof(f847,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f845,f108]) ).
fof(f849,plain,
( ! [X0] : multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_14 ),
inference(superposition,[],[f4,f132]) ).
fof(f855,plain,
( sk_c6 != sk_c6
| sk_c7 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f81,f132]) ).
fof(f856,plain,
( sk_c7 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f855]) ).
fof(f857,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f856,f123]) ).
fof(f858,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f900,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f201,f325]) ).
fof(f902,plain,
( identity = sk_c6
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f900,f3]) ).
fof(f903,plain,
( spl0_26
| ~ spl0_13
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f902,f130,f121,f836]) ).
fof(f915,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,multiply(identity,X0))
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f843,f837]) ).
fof(f916,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c5,X0)
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_demodulation,[],[f915,f1]) ).
fof(f924,plain,
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c6 != inverse(sk_c5)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_26 ),
inference(superposition,[],[f78,f916]) ).
fof(f925,plain,
( sk_c6 != inverse(sk_c5)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f924,f74]) ).
fof(f928,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26 ),
inference(forward_demodulation,[],[f925,f98]) ).
fof(f929,plain,
( identity != sk_c7
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26 ),
inference(forward_demodulation,[],[f928,f837]) ).
fof(f946,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c7,X0))
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f849,f837]) ).
fof(f947,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c7,X0)) = X0
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f946,f1]) ).
fof(f955,plain,
( sk_c8 = multiply(sk_c2,sk_c6)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_26 ),
inference(superposition,[],[f947,f74]) ).
fof(f957,plain,
( sk_c5 = multiply(sk_c2,identity)
| ~ spl0_9
| ~ spl0_14
| ~ spl0_26 ),
inference(superposition,[],[f947,f630]) ).
fof(f958,plain,
( sk_c2 = multiply(sk_c2,identity)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(superposition,[],[f947,f180]) ).
fof(f962,plain,
( sk_c8 = multiply(sk_c2,identity)
| ~ spl0_3
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f955,f837]) ).
fof(f970,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f201,f847]) ).
fof(f1010,plain,
( sk_c5 = sk_c2
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f958,f957]) ).
fof(f1020,plain,
( sk_c8 = multiply(sk_c5,identity)
| ~ spl0_3
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f962,f1010]) ).
fof(f1021,plain,
( sk_c8 = multiply(sk_c7,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1020,f916]) ).
fof(f1044,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f798,f847]) ).
fof(f1048,plain,
( identity = sk_c7
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1044,f837]) ).
fof(f1051,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1048,f929]) ).
fof(f1052,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1051]) ).
fof(f1054,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f74,f168]) ).
fof(f1071,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1054,f847]) ).
fof(f1093,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_26 ),
inference(superposition,[],[f1021,f1048]) ).
fof(f1094,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_demodulation,[],[f1093,f1]) ).
fof(f1107,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_21
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1094,f190]) ).
fof(f1108,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_21
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f1107]) ).
fof(f1122,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_7
| ~ spl0_9
| ~ spl0_18 ),
inference(forward_demodulation,[],[f844,f168]) ).
fof(f1126,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1071,f168]) ).
fof(f1130,plain,
( sk_c7 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1122,f847]) ).
fof(f1138,plain,
( sk_c8 = sk_c6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1130,f168]) ).
fof(f1142,plain,
( $false
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1138,f165]) ).
fof(f1143,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1142]) ).
fof(f1147,plain,
( sk_c7 != sk_c7
| sk_c7 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[],[f68,f89]) ).
fof(f1148,plain,
( sk_c7 != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f1147]) ).
fof(f1149,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f1148,f98]) ).
fof(f1150,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f1149]) ).
fof(f1181,plain,
( sk_c7 = multiply(inverse(sk_c7),sk_c6)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f201,f327]) ).
fof(f1237,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f1181,f796]) ).
fof(f1243,plain,
( sk_c8 != sk_c6
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f822,f108]) ).
fof(f1247,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1126,f167,f106,f101,f73,f163]) ).
fof(f1250,plain,
( spl0_18
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f1237,f96,f87,f73,f167]) ).
fof(f1252,plain,
( ~ spl0_17
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f1243,f167,f106,f101,f80,f163]) ).
fof(f1287,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c6)
| ~ spl0_3
| ~ spl0_18 ),
inference(superposition,[],[f796,f168]) ).
fof(f1291,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(superposition,[],[f970,f168]) ).
fof(f1294,plain,
( identity = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1291,f3]) ).
fof(f1297,plain,
( sk_c8 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1287,f164]) ).
fof(f1302,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f1294,f190]) ).
fof(f1303,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f1302]) ).
fof(f1304,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1297,f3]) ).
fof(f1307,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f1304,f190]) ).
fof(f1308,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f1307]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f85]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s21,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s22,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f142]) ).
cnf(s23,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s24,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s25,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s26,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s27,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f151]) ).
cnf(s28,plain,
( spl0_9
| spl0_16 ),
inference(sat_conversion,[],[f152]) ).
cnf(s29,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f153]) ).
cnf(s30,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f154]) ).
cnf(s31,plain,
( spl0_3
| spl0_16 ),
inference(sat_conversion,[],[f155]) ).
cnf(s32,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f159]) ).
cnf(s33,plain,
( ~ spl0_2
| ~ spl0_13
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( ~ spl0_2
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f191]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f366]) ).
cnf(s38,plain,
( ~ spl0_3
| ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f375]) ).
cnf(s42,plain,
( spl0_3
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f423]) ).
cnf(s46,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f443]) ).
cnf(s47,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f444]) ).
cnf(s48,plain,
( ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f445]) ).
cnf(s49,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| spl0_21 ),
inference(sat_conversion,[],[f452]) ).
cnf(s50,plain,
( ~ spl0_3
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| spl0_21 ),
inference(sat_conversion,[],[f458]) ).
cnf(s56,plain,
( spl0_7
| ~ spl0_9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f526]) ).
cnf(s58,plain,
( ~ spl0_4
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f541]) ).
cnf(s62,plain,
( ~ spl0_1
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f568]) ).
cnf(s65,plain,
( ~ spl0_6
| ~ spl0_15
| ~ spl0_16
| ~ spl0_21 ),
inference(sat_conversion,[],[f587]) ).
cnf(s67,plain,
( ~ spl0_13
| spl0_14
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f660]) ).
cnf(s69,plain,
( ~ spl0_11
| ~ spl0_18
| spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f677]) ).
cnf(s71,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18
| ~ spl0_21 ),
inference(sat_conversion,[],[f710]) ).
cnf(s78,plain,
( ~ spl0_6
| ~ spl0_10
| ~ spl0_11
| ~ spl0_21 ),
inference(sat_conversion,[],[f755]) ).
cnf(s85,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f858]) ).
cnf(s90,plain,
( ~ spl0_13
| ~ spl0_14
| spl0_26 ),
inference(sat_conversion,[],[f903]) ).
cnf(s97,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| ~ spl0_26 ),
inference(sat_conversion,[],[f1052]) ).
cnf(s100,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_18
| spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f1108]) ).
cnf(s105,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1143]) ).
cnf(s106,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s114,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_11
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1247]) ).
cnf(s117,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s119,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1252]) ).
cnf(s134,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f1303]) ).
cnf(s135,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18
| spl0_21 ),
inference(sat_conversion,[],[f1308]) ).
cnf(s136,plain,
spl0_3,
inference(rat,[],[s48,s47,s42,s6,s11,s16,s21,s26,s31]) ).
cnf(s137,plain,
( spl0_7
| ~ spl0_6 ),
inference(rat,[],[s49,s65,s38,s12,s17,s22,s27,s136]) ).
cnf(s138,plain,
( ~ spl0_16
| ~ spl0_15
| ~ spl0_14
| ~ spl0_13
| ~ spl0_6 ),
inference(rat,[],[s65,s50,s136]) ).
cnf(s139,plain,
( spl0_16
| ~ spl0_14
| ~ spl0_13
| ~ spl0_6 ),
inference(rat,[],[s100,s117,s78,s28,s29,s30,s137,s90,s136]) ).
cnf(s140,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_6 ),
inference(rat,[],[s100,s117,s78,s23,s24,s25,s138,s139,s90,s137,s136]) ).
cnf(s141,plain,
( spl0_14
| ~ spl0_6 ),
inference(rat,[],[s134,s117,s78,s18,s19,s20,s137,s136]) ).
cnf(s142,plain,
~ spl0_6,
inference(rat,[],[s134,s117,s78,s13,s14,s15,s140,s141,s137,s136]) ).
cnf(s143,plain,
( ~ spl0_13
| ~ spl0_5 ),
inference(rat,[],[s67,s134,s105,s117,s17,s18,s19,s20,s85,s136]) ).
cnf(s144,plain,
~ spl0_5,
inference(rat,[],[s119,s105,s117,s12,s13,s14,s15,s143,s136]) ).
cnf(s145,plain,
( spl0_9
| ~ spl0_21
| ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s58,s23,s28]) ).
cnf(s146,plain,
( spl0_16
| ~ spl0_7
| ~ spl0_9
| ~ spl0_26
| ~ spl0_4 ),
inference(rat,[],[s97,s29,s30,s117,s136]) ).
cnf(s147,plain,
( ~ spl0_7
| ~ spl0_21
| ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s97,s24,s25,s58,s146,s117,s90,s145,s136]) ).
cnf(s148,plain,
( ~ spl0_21
| ~ spl0_14
| ~ spl0_4
| ~ spl0_13 ),
inference(rat,[],[s56,s22,s27,s147,s145]) ).
cnf(s149,plain,
( ~ spl0_7
| ~ spl0_9
| ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s114,s24,s25,s135,s50,s117,s146,s90,s148,s136]) ).
cnf(s150,plain,
( ~ spl0_9
| ~ spl0_14
| ~ spl0_4
| ~ spl0_13 ),
inference(rat,[],[s56,s22,s27,s149]) ).
cnf(s151,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_4 ),
inference(rat,[],[s50,s23,s28,s150,s148,s136]) ).
cnf(s152,plain,
( ~ spl0_18
| ~ spl0_21
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s105,s71]) ).
cnf(s153,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s152,s134,s117,s17,s18,s19,s20,s136]) ).
cnf(s154,plain,
( ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s152,s134,s117,s12,s13,s14,s15,s151,s136]) ).
cnf(s155,plain,
~ spl0_4,
inference(rat,[],[s154,s153]) ).
cnf(s156,plain,
( ~ spl0_18
| ~ spl0_14
| ~ spl0_13
| ~ spl0_21
| ~ spl0_2 ),
inference(rat,[],[s37,s25,s30,s33,s69,s35,s136]) ).
cnf(s157,plain,
( ~ spl0_9
| spl0_18
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s56,s22,s27,s117,s136]) ).
cnf(s158,plain,
( ~ spl0_14
| ~ spl0_13
| ~ spl0_2
| ~ spl0_21 ),
inference(rat,[],[s46,s23,s28,s157,s156]) ).
cnf(s159,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s32,s19,s20]) ).
cnf(s160,plain,
( spl0_13
| ~ spl0_2 ),
inference(rat,[],[s32,s14,s15]) ).
cnf(s161,plain,
( spl0_10
| ~ spl0_2 ),
inference(rat,[],[s50,s24,s29,s158,s160,s159,s136]) ).
cnf(s162,plain,
( ~ spl0_13
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s50,s25,s30,s32,s161,s158,s136]) ).
cnf(s163,plain,
~ spl0_2,
inference(rat,[],[s162,s160,s159]) ).
cnf(s164,plain,
spl0_1,
inference(rat,[],[s1,s136,s142,s144,s155,s163]) ).
cnf(s165,plain,
( ~ spl0_9
| ~ spl0_14
| ~ spl0_13 ),
inference(rat,[],[s56,s22,s27,s106,s164]) ).
cnf(s166,plain,
( ~ spl0_14
| ~ spl0_13
| spl0_21 ),
inference(rat,[],[s50,s23,s28,s165,s136]) ).
cnf(s167,plain,
spl0_14,
inference(rat,[],[s106,s17,s18,s164]) ).
cnf(s168,plain,
spl0_13,
inference(rat,[],[s106,s12,s13,s164]) ).
cnf(s169,plain,
spl0_21,
inference(rat,[],[s166,s167,s168]) ).
cnf(s171,plain,
~ spl0_9,
inference(rat,[],[s165,s167,s168]) ).
cnf(s172,plain,
spl0_16,
inference(rat,[],[s28,s171]) ).
cnf(s173,plain,
spl0_15,
inference(rat,[],[s23,s171]) ).
cnf(s176,plain,
$false,
inference(rat,[],[s62,s164,s169,s168,s167,s172,s173]) ).
fof(f1309,plain,
$false,
inference(avatar_sat_refutation,[],[s176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 % Computer : n015.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 09:45:45 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.49 % (1409866)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (1409874)dis+10_1_sil=32000:sp=arity:random_seed=2196085338:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (1409872)% WARNING: option uhcvi not known.
% 0.17/0.49 % (1409871)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2862328140_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (1409872)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3907322819:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (1409873)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4081725634:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (1409875)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1391105509:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (1409876)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=410088822:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (1409877)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2731465457:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % TRYING [3]
% 0.17/0.49 % (1409874) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1409866-1409874"...
% 0.17/0.49 % TRYING [4]
% 0.17/0.49 % (1409874)...printing done.
% 0.17/0.49 % (1409874)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (1409874)------------------------------
% 0.17/0.49 % (1409874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (1409874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (1409874)CaDiCaL version: 2.1.3
% 0.17/0.49 % (1409874)Termination reason: Refutation
% 0.17/0.49 % (1409874)Time elapsed: 0.016 s
% 0.17/0.49 % (1409874)Peak memory usage: 12 MB
% 0.17/0.49 % (1409874)Instructions burned: 46 (million)
% 0.17/0.49 % (1409866)Success in time 0.045 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------