%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP269-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:20 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.42s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 49
% Syntax : Number of formulae : 383 ( 28 unt; 24 def)
% Number of atoms : 1430 ( 425 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2088 (1041 ~;1023 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 25 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f12,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c1,sk_c11) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f14]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = inverse(sk_c1)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c11 = inverse(sk_c1)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f33]) ).
fof(f43,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f44,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f52,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c11,sk_c9) = sk_c10
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f69,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c2,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f73]) ).
fof(f83,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = multiply(sk_c3,sk_c11) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( sk_c11 = inverse(sk_c2)
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c11 = inverse(sk_c2)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c2) = sk_c11
| multiply(sk_c5,sk_c8) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c11 = inverse(sk_c2)
| sk_c11 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c2) = sk_c11
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c11 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f93]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(X1,sk_c11) != sk_c9
| inverse(X1) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X2) != sk_c11
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,X5) != sk_c11
| inverse(X4) != X5
| multiply(X5,sk_c10) != sk_c11
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,X5)
| inverse(X4) != X5
| sk_c11 != multiply(X5,sk_c10)
| inverse(X6) != X7
| inverse(X7) != X5
| multiply(X6,X5) != X7 ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X6) != X7
| inverse(X4) != inverse(X7)
| multiply(X6,inverse(X4)) != X7 ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( sk_c10 != multiply(X0,sk_c11)
| inverse(X0) != sk_c11
| sk_c10 != multiply(sk_c11,sk_c9)
| sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c10)
| inverse(X4) != inverse(inverse(X6))
| inverse(X6) != multiply(X6,inverse(X4)) ),
inference(equality_resolution,[],[f105]) ).
fof(f108,definition,
( spl0_1
<=> ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f109,plain,
( ! [X6,X4] :
( sk_c11 != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,definition,
( spl0_2
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f112,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,definition,
( spl0_3
<=> ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f115,plain,
( ! [X2] :
( sk_c10 != multiply(X2,sk_c11)
| sk_c11 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,definition,
( spl0_4
<=> ! [X1] :
( sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f118,plain,
( ! [X1] :
( sk_c9 != multiply(X1,sk_c11)
| sk_c11 != inverse(X1) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,definition,
( spl0_5
<=> sk_c10 = multiply(sk_c11,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f121,plain,
( sk_c10 = multiply(sk_c11,sk_c9)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f122,plain,
( sk_c10 != multiply(sk_c11,sk_c9)
| spl0_5 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f106,f114,f120,f117,f114,f111,f108]) ).
fof(f129,definition,
( spl0_7
<=> sk_c11 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f131,plain,
( sk_c11 = inverse(sk_c2)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f149,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f151,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f149]) ).
fof(f152,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f94,f129,f149]) ).
fof(f154,definition,
( spl0_12
<=> sk_c11 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f156,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f92,f129,f154]) ).
fof(f159,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f161,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f90,f129,f159]) ).
fof(f164,definition,
( spl0_14
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f166,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f129,f164]) ).
fof(f169,definition,
( spl0_15
<=> sk_c11 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f171,plain,
( sk_c11 = inverse(sk_c3)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f129,f169]) ).
fof(f174,definition,
( spl0_16
<=> sk_c10 = multiply(sk_c3,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f176,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f177,plain,
( spl0_16
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f129,f174]) ).
fof(f179,definition,
( spl0_17
<=> sk_c9 = multiply(sk_c2,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c9 = multiply(sk_c2,sk_c11)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f179]) ).
fof(f186,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f74,f179,f149]) ).
fof(f187,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f72,f179,f154]) ).
fof(f188,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f70,f179,f159]) ).
fof(f190,plain,
( spl0_15
| spl0_17 ),
inference(avatar_split_clause,[],[f66,f179,f169]) ).
fof(f191,plain,
( spl0_16
| spl0_17 ),
inference(avatar_split_clause,[],[f64,f179,f174]) ).
fof(f196,plain,
( spl0_11
| spl0_5 ),
inference(avatar_split_clause,[],[f54,f120,f149]) ).
fof(f197,plain,
( spl0_12
| spl0_5 ),
inference(avatar_split_clause,[],[f52,f120,f154]) ).
fof(f198,plain,
( spl0_13
| spl0_5 ),
inference(avatar_split_clause,[],[f50,f120,f159]) ).
fof(f199,plain,
( spl0_14
| spl0_5 ),
inference(avatar_split_clause,[],[f48,f120,f164]) ).
fof(f200,plain,
( spl0_15
| spl0_5 ),
inference(avatar_split_clause,[],[f46,f120,f169]) ).
fof(f201,plain,
( spl0_16
| spl0_5 ),
inference(avatar_split_clause,[],[f44,f120,f174]) ).
fof(f203,definition,
( spl0_18
<=> sk_c11 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f205,plain,
( sk_c11 = inverse(sk_c1)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f203]) ).
fof(f210,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f34,f203,f149]) ).
fof(f211,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f32,f203,f154]) ).
fof(f217,definition,
( spl0_19
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f219,plain,
( multiply(sk_c1,sk_c11) = sk_c10
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f224,plain,
( spl0_11
| spl0_19 ),
inference(avatar_split_clause,[],[f15,f217,f149]) ).
fof(f225,plain,
( spl0_12
| spl0_19 ),
inference(avatar_split_clause,[],[f13,f217,f154]) ).
fof(f230,plain,
( identity = multiply(sk_c11,sk_c3)
| ~ spl0_15 ),
inference(superposition,[],[f3,f171]) ).
fof(f231,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_13 ),
inference(superposition,[],[f3,f161]) ).
fof(f237,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f243,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f237,f1]) ).
fof(f246,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f230]) ).
fof(f247,plain,
( ! [X0] : multiply(sk_c11,multiply(sk_c3,X0)) = X0
| ~ spl0_15 ),
inference(forward_demodulation,[],[f246,f1]) ).
fof(f260,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f247,f176]) ).
fof(f309,plain,
( sk_c10 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f243,f260]) ).
fof(f314,plain,
( sk_c10 = multiply(inverse(sk_c4),sk_c9)
| ~ spl0_14 ),
inference(superposition,[],[f243,f166]) ).
fof(f317,plain,
( sk_c8 = multiply(inverse(sk_c5),sk_c11)
| ~ spl0_12 ),
inference(superposition,[],[f243,f156]) ).
fof(f334,plain,
( sk_c8 = multiply(sk_c8,sk_c11)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f317,f151]) ).
fof(f337,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_demodulation,[],[f314,f161]) ).
fof(f341,plain,
( identity = sk_c10
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f309,f3]) ).
fof(f374,plain,
( sk_c11 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f243,f334]) ).
fof(f376,plain,
( identity = sk_c11
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f374,f3]) ).
fof(f381,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f230,f376]) ).
fof(f390,plain,
( identity = sk_c3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f381,f1]) ).
fof(f396,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f337,f341]) ).
fof(f397,plain,
( identity = sk_c9
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f396,f1]) ).
fof(f399,plain,
( sk_c10 != multiply(sk_c11,identity)
| spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f122,f397]) ).
fof(f400,plain,
( sk_c10 != multiply(identity,identity)
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f399,f376]) ).
fof(f402,plain,
( identity != sk_c10
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f400,f1]) ).
fof(f403,plain,
( $false
| spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f402,f341]) ).
fof(f404,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f405,plain,
( ! [X2] :
( sk_c10 != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f115,f376]) ).
fof(f407,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c11 != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f405,f341]) ).
fof(f409,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f407,f376]) ).
fof(f411,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f409,f1]) ).
fof(f416,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f411]) ).
fof(f430,plain,
( sk_c11 = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f171,f390]) ).
fof(f431,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15 ),
inference(forward_demodulation,[],[f430,f376]) ).
fof(f479,plain,
( $false
| ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f431,f416]) ).
fof(f480,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f479]) ).
fof(f481,plain,
( identity = inverse(sk_c2)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f131,f376]) ).
fof(f487,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f121,f376]) ).
fof(f491,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f487,f1]) ).
fof(f494,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f3,f481]) ).
fof(f495,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f494,f1]) ).
fof(f517,plain,
( sk_c11 = multiply(inverse(sk_c2),sk_c9)
| ~ spl0_17 ),
inference(superposition,[],[f243,f181]) ).
fof(f519,plain,
( sk_c11 = multiply(sk_c11,sk_c9)
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f517,f131]) ).
fof(f520,plain,
( sk_c11 = multiply(inverse(sk_c1),sk_c10)
| ~ spl0_19 ),
inference(superposition,[],[f243,f219]) ).
fof(f522,plain,
( sk_c11 = multiply(sk_c11,sk_c10)
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f520,f205]) ).
fof(f526,plain,
( sk_c11 != sk_c10
| sk_c11 != inverse(identity)
| ~ spl0_3 ),
inference(superposition,[],[f115,f1]) ).
fof(f529,plain,
( sk_c10 != sk_c10
| sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_19 ),
inference(superposition,[],[f115,f219]) ).
fof(f531,plain,
( sk_c11 != inverse(sk_c1)
| ~ spl0_3
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f529]) ).
fof(f533,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f531,f205]) ).
fof(f534,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f533]) ).
fof(f540,definition,
( spl0_23
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f541,plain,
( identity = sk_c10
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f542,plain,
( identity != sk_c10
| spl0_23 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f545,definition,
( spl0_24
<=> sk_c11 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f546,plain,
( sk_c11 = inverse(identity)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f547,plain,
( sk_c11 != inverse(identity)
| spl0_24 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f549,definition,
( spl0_25
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f550,plain,
( sk_c11 = sk_c10
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( ~ spl0_24
| ~ spl0_25
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f526,f114,f549,f545]) ).
fof(f554,plain,
( spl0_23
| ~ spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f341,f174,f169,f540]) ).
fof(f561,plain,
( sk_c11 = inverse(identity)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f131,f495]) ).
fof(f562,plain,
( spl0_24
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f561,f154,f149,f129,f545]) ).
fof(f565,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f481,f495]) ).
fof(f568,plain,
( identity = multiply(identity,sk_c4)
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f231,f541]) ).
fof(f573,plain,
( identity = sk_c4
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f568,f1]) ).
fof(f603,plain,
( sk_c10 = inverse(identity)
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f161,f573]) ).
fof(f625,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_23 ),
inference(forward_demodulation,[],[f112,f541]) ).
fof(f626,plain,
( ! [X3] :
( sk_c10 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f625,f491]) ).
fof(f627,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f626,f541]) ).
fof(f628,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f627,f541]) ).
fof(f629,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f628,f1]) ).
fof(f631,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f628,f3]) ).
fof(f635,plain,
( identity != inverse(inverse(identity))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f631]) ).
fof(f636,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f629]) ).
fof(f637,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f635,f565]) ).
fof(f640,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f637,f565]) ).
fof(f641,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f640]) ).
fof(f644,plain,
( identity = inverse(identity)
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f603,f541]) ).
fof(f678,plain,
( identity = inverse(identity)
| ~ spl0_11
| ~ spl0_12
| ~ spl0_24 ),
inference(forward_demodulation,[],[f546,f376]) ).
fof(f680,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f678,f636]) ).
fof(f681,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f682,plain,
( ! [X6,X4] :
( identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f109,f376]) ).
fof(f683,plain,
( ! [X6,X4] :
( sk_c11 != multiply(inverse(X4),identity)
| identity != multiply(X4,inverse(X4))
| inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f682,f541]) ).
fof(f684,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| identity != multiply(X4,inverse(X4))
| identity != multiply(inverse(X4),identity)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f683,f376]) ).
fof(f690,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c10)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(superposition,[],[f684,f161]) ).
fof(f694,plain,
( ! [X0] :
( inverse(X0) != inverse(inverse(identity))
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity)
| inverse(X0) != inverse(identity) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f684,f1]) ).
fof(f698,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity)
| inverse(X0) != inverse(inverse(identity)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f694,f678]) ).
fof(f713,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c4,sk_c10)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_23 ),
inference(forward_demodulation,[],[f690,f541]) ).
fof(f716,plain,
( ! [X0] :
( inverse(X0) != inverse(identity)
| identity != inverse(X0)
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f698,f678]) ).
fof(f726,plain,
( ! [X0] :
( identity != sk_c9
| inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_23 ),
inference(forward_demodulation,[],[f713,f166]) ).
fof(f728,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != inverse(X0)
| identity != multiply(X0,inverse(X0))
| identity != multiply(inverse(X0),identity) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f716,f678]) ).
fof(f729,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0))
| identity != inverse(X0) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(duplicate_literal_removal,[],[f728]) ).
fof(f731,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != multiply(sk_c10,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f726,f397]) ).
fof(f734,plain,
( ! [X0] :
( identity != multiply(identity,identity)
| inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f731,f541]) ).
fof(f736,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c10 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f734,f1]) ).
fof(f738,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(forward_demodulation,[],[f736,f541]) ).
fof(f790,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23 ),
inference(superposition,[],[f738,f3]) ).
fof(f801,definition,
( spl0_32
<=> identity = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f802,plain,
( identity = inverse(sk_c2)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f803,plain,
( identity != inverse(sk_c2)
| spl0_32 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f825,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f790,f678]) ).
fof(f827,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f825,f678]) ).
fof(f829,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f827,f678]) ).
fof(f832,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_demodulation,[],[f829,f678]) ).
fof(f833,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f832,f678]) ).
fof(f834,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f833]) ).
fof(f835,plain,
( identity != inverse(identity)
| ~ spl0_11
| ~ spl0_12
| spl0_24 ),
inference(forward_demodulation,[],[f547,f376]) ).
fof(f846,definition,
( spl0_39
<=> identity = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_39])],[avatar_definition]) ).
fof(f847,plain,
( identity = inverse(identity)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f850,plain,
( ~ spl0_39
| ~ spl0_11
| ~ spl0_12
| spl0_24 ),
inference(avatar_split_clause,[],[f835,f545,f154,f149,f846]) ).
fof(f867,plain,
( ! [X1] :
( sk_c9 != multiply(X1,identity)
| sk_c11 != inverse(X1) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f118,f376]) ).
fof(f870,plain,
( spl0_39
| ~ spl0_13
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f644,f540,f159,f846]) ).
fof(f871,plain,
( ! [X1] :
( sk_c10 != multiply(X1,identity)
| sk_c11 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f867,f491]) ).
fof(f872,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| sk_c11 != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f871,f541]) ).
fof(f873,plain,
( ! [X1] :
( identity != multiply(X1,identity)
| identity != inverse(X1) )
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(forward_demodulation,[],[f872,f376]) ).
fof(f874,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(superposition,[],[f873,f1]) ).
fof(f887,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f874]) ).
fof(f890,plain,
( ~ spl0_39
| ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f887,f540,f154,f149,f120,f117,f846]) ).
fof(f900,plain,
( identity = inverse(sk_c2)
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f131,f376]) ).
fof(f901,plain,
( spl0_39
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f565,f154,f149,f129,f846]) ).
fof(f921,plain,
( spl0_32
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f900,f154,f149,f129,f801]) ).
fof(f1016,plain,
( identity != identity
| identity != multiply(identity,inverse(identity))
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(superposition,[],[f729,f3]) ).
fof(f1017,plain,
( identity != multiply(identity,inverse(identity))
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f1016]) ).
fof(f1020,plain,
( identity != multiply(identity,inverse(identity))
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f1017,f847]) ).
fof(f1026,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24
| ~ spl0_39 ),
inference(forward_demodulation,[],[f1020,f1]) ).
fof(f1028,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24
| ~ spl0_39 ),
inference(forward_subsumption_resolution,[],[f1026,f847]) ).
fof(f1029,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24
| ~ spl0_39 ),
inference(avatar_contradiction_clause,[],[f1028]) ).
fof(f1099,plain,
( identity = sk_c11
| ~ spl0_7
| ~ spl0_32 ),
inference(forward_demodulation,[],[f131,f802]) ).
fof(f1104,plain,
( identity = multiply(sk_c11,sk_c2)
| ~ spl0_7 ),
inference(superposition,[],[f3,f131]) ).
fof(f1115,plain,
( identity != sk_c11
| ~ spl0_7
| spl0_32 ),
inference(forward_demodulation,[],[f803,f131]) ).
fof(f1121,plain,
( sk_c9 != sk_c9
| sk_c11 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_17 ),
inference(superposition,[],[f118,f181]) ).
fof(f1122,plain,
( sk_c11 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f1121]) ).
fof(f1123,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f1122,f131]) ).
fof(f1124,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f1123]) ).
fof(f1128,definition,
( spl0_43
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_43])],[avatar_definition]) ).
fof(f1129,plain,
( identity = sk_c9
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f1168,definition,
( spl0_47
<=> ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_47])],[avatar_definition]) ).
fof(f1169,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1171,definition,
( spl0_48
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_48])],[avatar_definition]) ).
fof(f1172,plain,
( sk_c11 = sk_c9
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f1173,plain,
( sk_c11 != sk_c9
| spl0_48 ),
inference(avatar_component_clause,[],[f1171]) ).
fof(f1198,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f519,f121]) ).
fof(f1199,plain,
( sk_c11 = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f121,f519]) ).
fof(f1200,plain,
( sk_c9 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f243,f519]) ).
fof(f1203,plain,
( identity = sk_c9
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f1200,f3]) ).
fof(f1205,plain,
( identity = sk_c11
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f1198,f541]) ).
fof(f1206,plain,
( spl0_43
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1203,f179,f129,f1128]) ).
fof(f1209,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| spl0_32 ),
inference(forward_subsumption_resolution,[],[f1205,f1115]) ).
fof(f1210,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| spl0_32 ),
inference(avatar_contradiction_clause,[],[f1209]) ).
fof(f1225,plain,
( identity = multiply(identity,sk_c2)
| ~ spl0_7
| ~ spl0_32 ),
inference(superposition,[],[f1104,f1099]) ).
fof(f1231,plain,
( identity = sk_c2
| ~ spl0_7
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1225,f1]) ).
fof(f1242,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_7
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1169,f1099]) ).
fof(f1245,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,identity)
| identity != inverse(inverse(X0)) )
| ~ spl0_7
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1242,f1099]) ).
fof(f1269,plain,
( identity = sk_c11
| ~ spl0_43
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1172,f1129]) ).
fof(f1319,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_32 ),
inference(forward_demodulation,[],[f802,f1231]) ).
fof(f1320,plain,
( spl0_39
| ~ spl0_7
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1319,f801,f129,f846]) ).
fof(f1323,plain,
( identity != inverse(inverse(identity))
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_7
| ~ spl0_32
| ~ spl0_47 ),
inference(superposition,[],[f1245,f3]) ).
fof(f1328,plain,
( identity != inverse(sk_c11)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1323,f546]) ).
fof(f1331,plain,
( identity != inverse(identity)
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1328,f1099]) ).
fof(f1334,plain,
( identity != sk_c11
| identity != inverse(inverse(inverse(identity)))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1331,f546]) ).
fof(f1337,plain,
( identity != inverse(inverse(inverse(identity)))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1334,f1099]) ).
fof(f1340,plain,
( identity != inverse(inverse(sk_c11))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1337,f546]) ).
fof(f1344,plain,
( identity != inverse(inverse(identity))
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1340,f1099]) ).
fof(f1347,plain,
( identity != inverse(sk_c11)
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1344,f546]) ).
fof(f1348,plain,
( identity != inverse(identity)
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1347,f1099]) ).
fof(f1349,plain,
( identity != sk_c11
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_demodulation,[],[f1348,f546]) ).
fof(f1350,plain,
( $false
| ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(forward_subsumption_resolution,[],[f1349,f1099]) ).
fof(f1351,plain,
( ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(avatar_contradiction_clause,[],[f1350]) ).
fof(f1352,plain,
( identity != inverse(identity)
| ~ spl0_7
| spl0_24
| ~ spl0_32 ),
inference(forward_demodulation,[],[f547,f1099]) ).
fof(f1358,plain,
( ~ spl0_39
| ~ spl0_7
| spl0_24
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1352,f801,f545,f129,f846]) ).
fof(f1362,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_2
| ~ spl0_23
| ~ spl0_43 ),
inference(forward_demodulation,[],[f625,f1129]) ).
fof(f1374,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_23
| ~ spl0_43 ),
inference(forward_demodulation,[],[f1362,f541]) ).
fof(f1391,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_2
| ~ spl0_23
| ~ spl0_43 ),
inference(superposition,[],[f1374,f1]) ).
fof(f1396,plain,
( identity != inverse(identity)
| ~ spl0_2
| ~ spl0_23
| ~ spl0_43 ),
inference(trivial_inequality_removal,[],[f1391]) ).
fof(f1398,plain,
( ~ spl0_39
| ~ spl0_2
| ~ spl0_23
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f1396,f1128,f540,f111,f846]) ).
fof(f1407,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_32 ),
inference(forward_demodulation,[],[f1199,f1099]) ).
fof(f1421,plain,
( spl0_23
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1407,f801,f179,f129,f120,f540]) ).
fof(f1433,plain,
( spl0_25
| ~ spl0_5
| ~ spl0_7
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f1199,f179,f129,f120,f549]) ).
fof(f1438,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_5
| ~ spl0_43
| ~ spl0_48 ),
inference(superposition,[],[f121,f1269]) ).
fof(f1449,plain,
( sk_c10 = sk_c9
| ~ spl0_5
| ~ spl0_43
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1438,f1]) ).
fof(f1451,plain,
( identity = sk_c10
| ~ spl0_5
| ~ spl0_43
| ~ spl0_48 ),
inference(forward_demodulation,[],[f1449,f1129]) ).
fof(f1452,plain,
( $false
| ~ spl0_5
| spl0_23
| ~ spl0_43
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[],[f1451,f542]) ).
fof(f1453,plain,
( ~ spl0_5
| spl0_23
| ~ spl0_43
| ~ spl0_48 ),
inference(avatar_contradiction_clause,[],[f1452]) ).
fof(f1454,plain,
( identity != sk_c11
| ~ spl0_43
| spl0_48 ),
inference(forward_demodulation,[],[f1173,f1129]) ).
fof(f1459,plain,
( ! [X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| sk_c11 != multiply(X4,inverse(X4))
| sk_c11 != multiply(inverse(X4),sk_c11)
| inverse(X4) != inverse(inverse(X6)) )
| ~ spl0_1
| ~ spl0_25 ),
inference(forward_demodulation,[],[f109,f550]) ).
fof(f1460,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c1,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_25 ),
inference(superposition,[],[f1459,f205]) ).
fof(f1473,plain,
( ! [X0] :
( sk_c11 != sk_c10
| inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f1460,f219]) ).
fof(f1475,plain,
( ! [X0] :
( inverse(X0) != multiply(X0,sk_c11)
| sk_c11 != multiply(sk_c11,sk_c11)
| sk_c11 != inverse(inverse(X0)) )
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1473,f550]) ).
fof(f1477,definition,
( spl0_52
<=> sk_c11 = multiply(sk_c11,sk_c11) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f1478,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1477]) ).
fof(f1480,plain,
( ~ spl0_52
| spl0_47
| ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1475,f549,f217,f203,f108,f1168,f1477]) ).
fof(f1490,plain,
( sk_c11 = multiply(sk_c11,sk_c11)
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(forward_demodulation,[],[f522,f550]) ).
fof(f1493,plain,
( spl0_52
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1490,f549,f217,f203,f1477]) ).
fof(f1494,plain,
( sk_c11 = multiply(inverse(sk_c11),sk_c11)
| ~ spl0_52 ),
inference(superposition,[],[f243,f1478]) ).
fof(f1496,plain,
( identity = sk_c11
| ~ spl0_52 ),
inference(forward_demodulation,[],[f1494,f3]) ).
fof(f1497,plain,
( $false
| ~ spl0_43
| spl0_48
| ~ spl0_52 ),
inference(forward_subsumption_resolution,[],[f1496,f1454]) ).
fof(f1498,plain,
( ~ spl0_43
| spl0_48
| ~ spl0_52 ),
inference(avatar_contradiction_clause,[],[f1497]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f123]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f157]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f162]) ).
cnf(s10,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f167]) ).
cnf(s11,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f172]) ).
cnf(s12,plain,
( spl0_7
| spl0_16 ),
inference(sat_conversion,[],[f177]) ).
cnf(s17,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f186]) ).
cnf(s18,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s19,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s21,plain,
( spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s22,plain,
( spl0_16
| spl0_17 ),
inference(sat_conversion,[],[f191]) ).
cnf(s27,plain,
( spl0_5
| spl0_11 ),
inference(sat_conversion,[],[f196]) ).
cnf(s28,plain,
( spl0_5
| spl0_12 ),
inference(sat_conversion,[],[f197]) ).
cnf(s29,plain,
( spl0_5
| spl0_13 ),
inference(sat_conversion,[],[f198]) ).
cnf(s30,plain,
( spl0_5
| spl0_14 ),
inference(sat_conversion,[],[f199]) ).
cnf(s31,plain,
( spl0_5
| spl0_15 ),
inference(sat_conversion,[],[f200]) ).
cnf(s32,plain,
( spl0_5
| spl0_16 ),
inference(sat_conversion,[],[f201]) ).
cnf(s37,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f210]) ).
cnf(s38,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f211]) ).
cnf(s47,plain,
( spl0_11
| spl0_19 ),
inference(sat_conversion,[],[f224]) ).
cnf(s48,plain,
( spl0_12
| spl0_19 ),
inference(sat_conversion,[],[f225]) ).
cnf(s53,plain,
( spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f404]) ).
cnf(s55,plain,
( ~ spl0_3
| ~ spl0_11
| ~ spl0_12
| ~ spl0_15
| ~ spl0_16 ),
inference(sat_conversion,[],[f480]) ).
cnf(s58,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_19 ),
inference(sat_conversion,[],[f534]) ).
cnf(s60,plain,
( ~ spl0_3
| ~ spl0_24
| ~ spl0_25 ),
inference(sat_conversion,[],[f552]) ).
cnf(s63,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_23 ),
inference(sat_conversion,[],[f554]) ).
cnf(s66,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_24 ),
inference(sat_conversion,[],[f562]) ).
cnf(s68,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23 ),
inference(sat_conversion,[],[f641]) ).
cnf(s69,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f681]) ).
cnf(s79,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_23
| ~ spl0_24 ),
inference(sat_conversion,[],[f834]) ).
cnf(s82,plain,
( ~ spl0_11
| ~ spl0_12
| spl0_24
| ~ spl0_39 ),
inference(sat_conversion,[],[f850]) ).
cnf(s86,plain,
( ~ spl0_13
| ~ spl0_23
| spl0_39 ),
inference(sat_conversion,[],[f870]) ).
cnf(s91,plain,
( ~ spl0_4
| ~ spl0_5
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_39 ),
inference(sat_conversion,[],[f890]) ).
cnf(s93,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_39 ),
inference(sat_conversion,[],[f901]) ).
cnf(s96,plain,
( ~ spl0_7
| ~ spl0_11
| ~ spl0_12
| spl0_32 ),
inference(sat_conversion,[],[f921]) ).
cnf(s112,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| ~ spl0_23
| ~ spl0_24
| ~ spl0_39 ),
inference(sat_conversion,[],[f1029]) ).
cnf(s120,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_17 ),
inference(sat_conversion,[],[f1124]) ).
cnf(s128,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_43 ),
inference(sat_conversion,[],[f1206]) ).
cnf(s130,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| ~ spl0_23
| spl0_32 ),
inference(sat_conversion,[],[f1210]) ).
cnf(s141,plain,
( ~ spl0_7
| ~ spl0_32
| spl0_39 ),
inference(sat_conversion,[],[f1320]) ).
cnf(s145,plain,
( ~ spl0_7
| ~ spl0_24
| ~ spl0_32
| ~ spl0_47 ),
inference(sat_conversion,[],[f1351]) ).
cnf(s148,plain,
( ~ spl0_7
| spl0_24
| ~ spl0_32
| ~ spl0_39 ),
inference(sat_conversion,[],[f1358]) ).
cnf(s154,plain,
( ~ spl0_2
| ~ spl0_23
| ~ spl0_39
| ~ spl0_43 ),
inference(sat_conversion,[],[f1398]) ).
cnf(s158,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| spl0_23
| ~ spl0_32 ),
inference(sat_conversion,[],[f1421]) ).
cnf(s166,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_17
| spl0_25 ),
inference(sat_conversion,[],[f1433]) ).
cnf(s168,plain,
( ~ spl0_5
| spl0_23
| ~ spl0_43
| ~ spl0_48 ),
inference(sat_conversion,[],[f1453]) ).
cnf(s170,plain,
( ~ spl0_1
| ~ spl0_18
| ~ spl0_19
| ~ spl0_25
| spl0_47
| ~ spl0_52 ),
inference(sat_conversion,[],[f1480]) ).
cnf(s173,plain,
( ~ spl0_18
| ~ spl0_19
| ~ spl0_25
| spl0_52 ),
inference(sat_conversion,[],[f1493]) ).
cnf(s174,plain,
( ~ spl0_43
| spl0_48
| ~ spl0_52 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s175,plain,
spl0_5,
inference(rat,[],[s53,s27,s28,s29,s30,s31,s32]) ).
cnf(s176,plain,
( spl0_7
| ~ spl0_4 ),
inference(rat,[],[s91,s86,s63,s7,s8,s9,s11,s12,s175]) ).
cnf(s177,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s91,s86,s63,s17,s18,s19,s21,s22,s120,s175]) ).
cnf(s178,plain,
~ spl0_4,
inference(rat,[],[s177,s176]) ).
cnf(s179,plain,
( spl0_7
| ~ spl0_3 ),
inference(rat,[],[s55,s7,s8,s11,s12]) ).
cnf(s180,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_3 ),
inference(rat,[],[s55,s21,s22,s166,s60,s82,s93,s179,s175]) ).
cnf(s181,plain,
( spl0_12
| ~ spl0_3 ),
inference(rat,[],[s58,s38,s48]) ).
cnf(s182,plain,
( ~ spl0_12
| ~ spl0_3 ),
inference(rat,[],[s58,s37,s47,s180]) ).
cnf(s183,plain,
~ spl0_3,
inference(rat,[],[s182,s181]) ).
cnf(s184,plain,
( spl0_23
| ~ spl0_32
| ~ spl0_7 ),
inference(rat,[],[s63,s21,s22,s158,s175]) ).
cnf(s185,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_2
| ~ spl0_11 ),
inference(rat,[],[s184,s96,s68,s175]) ).
cnf(s186,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_2 ),
inference(rat,[],[s82,s69,s86,s63,s9,s11,s12,s185,s175]) ).
cnf(s187,plain,
( spl0_12
| ~ spl0_2 ),
inference(rat,[],[s141,s154,s130,s168,s174,s173,s166,s128,s8,s18,s38,s48,s175]) ).
cnf(s188,plain,
( ~ spl0_12
| ~ spl0_2 ),
inference(rat,[],[s141,s154,s130,s168,s174,s173,s166,s128,s7,s17,s37,s47,s186,s175]) ).
cnf(s189,plain,
~ spl0_2,
inference(rat,[],[s188,s187]) ).
cnf(s190,plain,
spl0_1,
inference(rat,[],[s2,s175,s178,s183,s189]) ).
cnf(s191,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s184,s112,s96,s66,s93,s190]) ).
cnf(s192,plain,
( ~ spl0_12
| ~ spl0_11 ),
inference(rat,[],[s82,s79,s86,s63,s9,s10,s11,s12,s191,s190]) ).
cnf(s193,plain,
spl0_12,
inference(rat,[],[s145,s148,s141,s130,s168,s174,s170,s173,s166,s128,s8,s18,s38,s48,s175,s190]) ).
cnf(s194,plain,
~ spl0_11,
inference(rat,[],[s192,s193]) ).
cnf(s195,plain,
spl0_19,
inference(rat,[],[s47,s194]) ).
cnf(s196,plain,
spl0_18,
inference(rat,[],[s37,s194]) ).
cnf(s197,plain,
spl0_17,
inference(rat,[],[s17,s194]) ).
cnf(s198,plain,
spl0_7,
inference(rat,[],[s7,s194]) ).
cnf(s199,plain,
spl0_43,
inference(rat,[],[s128,s198,s197]) ).
cnf(s200,plain,
spl0_25,
inference(rat,[],[s166,s198,s175,s197]) ).
cnf(s202,plain,
spl0_52,
inference(rat,[],[s173,s196,s195,s200]) ).
cnf(s203,plain,
spl0_47,
inference(rat,[],[s170,s202,s196,s195,s190,s200]) ).
cnf(s204,plain,
spl0_48,
inference(rat,[],[s174,s199,s202]) ).
cnf(s205,plain,
spl0_23,
inference(rat,[],[s168,s199,s175,s204]) ).
cnf(s206,plain,
spl0_32,
inference(rat,[],[s130,s197,s198,s175,s205]) ).
cnf(s207,plain,
spl0_39,
inference(rat,[],[s141,s198,s206]) ).
cnf(s208,plain,
spl0_24,
inference(rat,[],[s148,s207,s198,s206]) ).
cnf(s209,plain,
$false,
inference(rat,[],[s145,s203,s198,s208,s206]) ).
fof(f1499,plain,
$false,
inference(avatar_sat_refutation,[],[s209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP269-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.33 % Computer : n006.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 27 09:43:40 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 Running first-order model finding
% 0.11/0.37 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42 % (2740938)Will run a generic schedule for satisfiability detection.
% 0.11/0.42 % (2740946)dis+10_1_sil=32000:sp=arity:random_seed=4032909104:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.42 % (2740944)% WARNING: option uhcvi not known.
% 0.11/0.42 % (2740945)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2059391273:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.42 % (2740943)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2849356766_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.42 % (2740944)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=563099290:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.42 % (2740947)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2157099733:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.42 % (2740948)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3174478073:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.42 % (2740949)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1659565143:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.42 % TRYING [1]
% 0.11/0.42 % TRYING [2]
% 0.11/0.42 % (2740946) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2740938-2740946"...
% 0.11/0.42 % TRYING [3]
% 0.11/0.42 % (2740946)...printing done.
% 0.11/0.42 % (2740946)Refutation found. Thanks to Tanya!
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.42 % (2740946)------------------------------
% 0.11/0.42 % (2740946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.42 % (2740946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.42 % (2740946)CaDiCaL version: 2.1.3
% 0.11/0.42 % (2740946)Termination reason: Refutation
% 0.11/0.42 % (2740946)Time elapsed: 0.017 s
% 0.11/0.42 % (2740946)Peak memory usage: 13 MB
% 0.11/0.42 % (2740946)Instructions burned: 52 (million)
% 0.11/0.42 % (2740938)Success in time 0.043 s
% 0.11/0.42 % Vampire exiting
%------------------------------------------------------------------------------