%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP209-1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:10 AM UTC 2026
% Result : Unsatisfiable 0.65s 0.61s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 45
% Syntax : Number of formulae : 316 ( 19 unt; 19 def)
% Number of atoms : 1087 ( 349 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1531 ( 760 ~; 752 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 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(f9,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f23,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c2 = inverse(sk_c1)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c2 = inverse(sk_c1)
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f47,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c10,sk_c4) = sk_c9
| multiply(sk_c5,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| sk_c10 = multiply(sk_c5,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f61,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f65,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c3,sk_c10) = sk_c4
| multiply(sk_c8,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| sk_c9 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c5) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = inverse(sk_c5) ),
inference(reorient_equations,[],[f75]) ).
fof(f79,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c6,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c10 = inverse(sk_c3)
| sk_c10 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c3) = sk_c10
| inverse(sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c10 = inverse(sk_c3)
| sk_c8 = inverse(sk_c7) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( inverse(sk_c3) = sk_c10
| multiply(sk_c8,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c10 = inverse(sk_c3)
| sk_c9 = multiply(sk_c8,sk_c10) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| multiply(X1,sk_c9) != sk_c10
| multiply(sk_c10,X2) != sk_c9
| multiply(X3,sk_c10) != X2
| inverse(X3) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c9
| multiply(X6,X7) != sk_c9
| inverse(X6) != X7
| multiply(X7,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X0,X1) != sk_c10
| inverse(X0) != X1
| sk_c10 != multiply(X1,sk_c9)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,X2)
| multiply(X3,sk_c10) != X2
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f90]) ).
fof(f92,plain,
! [X3,X0,X6,X7,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,X7)
| inverse(X6) != X7
| sk_c9 != multiply(X7,sk_c10) ),
inference(equality_resolution,[],[f91]) ).
fof(f93,plain,
! [X3,X0,X6,X4,X5] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3)
| sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5)
| sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) ),
inference(equality_resolution,[],[f92]) ).
fof(f95,definition,
( spl0_1
<=> ! [X6] :
( sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f96,plain,
( ! [X6] :
( sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_2
<=> ! [X5] :
( sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f99,plain,
( ! [X5] :
( sk_c10 != multiply(X5,sk_c9)
| sk_c9 != inverse(X5) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_3
<=> ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f102,plain,
( ! [X4] :
( sk_c10 != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,definition,
( spl0_4
<=> ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f105,plain,
( ! [X3] :
( sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != inverse(X3) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,definition,
( spl0_5
<=> ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f108,plain,
( ! [X0] :
( sk_c10 != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f109,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(avatar_split_clause,[],[f93,f107,f104,f101,f98,f95]) ).
fof(f111,definition,
( spl0_6
<=> sk_c9 = multiply(sk_c8,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f113,plain,
( sk_c9 = multiply(sk_c8,sk_c10)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f115,definition,
( spl0_7
<=> sk_c10 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f117,plain,
( sk_c10 = inverse(sk_c3)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f115,f111]) ).
fof(f120,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f122,plain,
( sk_c8 = inverse(sk_c7)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f115,f120]) ).
fof(f125,definition,
( spl0_9
<=> sk_c9 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f127,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f125]) ).
fof(f128,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f115,f125]) ).
fof(f130,definition,
( spl0_10
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f132,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f115,f130]) ).
fof(f135,definition,
( spl0_11
<=> sk_c10 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f137,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f115,f135]) ).
fof(f140,definition,
( spl0_12
<=> sk_c10 = multiply(sk_c5,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f142,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f145,definition,
( spl0_13
<=> sk_c10 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f147,plain,
( sk_c10 = inverse(sk_c5)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f115,f145]) ).
fof(f150,definition,
( spl0_14
<=> sk_c4 = multiply(sk_c3,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f152,plain,
( sk_c4 = multiply(sk_c3,sk_c10)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f150,f111]) ).
fof(f154,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f150,f120]) ).
fof(f155,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f150,f125]) ).
fof(f156,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f150,f130]) ).
fof(f157,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f150,f135]) ).
fof(f159,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f150,f145]) ).
fof(f161,definition,
( spl0_15
<=> sk_c9 = multiply(sk_c10,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f162,plain,
( sk_c9 != multiply(sk_c10,sk_c4)
| spl0_15 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f163,plain,
( sk_c9 = multiply(sk_c10,sk_c4)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f169,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f50,f161,f140]) ).
fof(f170,plain,
( spl0_13
| spl0_15 ),
inference(avatar_split_clause,[],[f48,f161,f145]) ).
fof(f183,definition,
( spl0_17
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f185,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,plain,
( spl0_8
| spl0_17 ),
inference(avatar_split_clause,[],[f30,f183,f120]) ).
fof(f188,plain,
( spl0_9
| spl0_17 ),
inference(avatar_split_clause,[],[f28,f183,f125]) ).
fof(f189,plain,
( spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f26,f183,f130]) ).
fof(f190,plain,
( spl0_11
| spl0_17 ),
inference(avatar_split_clause,[],[f24,f183,f135]) ).
fof(f194,definition,
( spl0_18
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f196,plain,
( multiply(sk_c1,sk_c2) = sk_c10
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f194,f120]) ).
fof(f199,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f194,f125]) ).
fof(f200,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f194,f130]) ).
fof(f201,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f194,f135]) ).
fof(f205,plain,
( sk_c10 != sk_c10
| sk_c9 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(superposition,[],[f99,f137]) ).
fof(f206,plain,
( sk_c9 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f205]) ).
fof(f211,plain,
( ~ spl0_10
| ~ spl0_2
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f206,f135,f98,f130]) ).
fof(f215,plain,
( identity = multiply(sk_c2,sk_c1)
| ~ spl0_17 ),
inference(superposition,[],[f3,f185]) ).
fof(f217,plain,
( identity = multiply(sk_c8,sk_c7)
| ~ spl0_8 ),
inference(superposition,[],[f3,f122]) ).
fof(f218,plain,
( identity = multiply(sk_c10,sk_c3)
| ~ spl0_7 ),
inference(superposition,[],[f3,f117]) ).
fof(f225,definition,
( spl0_20
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
fof(f226,plain,
( identity = sk_c10
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f231,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f232,plain,
( ! [X0] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c10,X0)
| ~ spl0_18 ),
inference(superposition,[],[f4,f196]) ).
fof(f240,plain,
( ! [X0,X1] :
( sk_c10 != multiply(X0,multiply(X1,sk_c9))
| sk_c9 != inverse(multiply(X0,X1)) )
| ~ spl0_2 ),
inference(superposition,[],[f99,f4]) ).
fof(f241,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f231,f1]) ).
fof(f244,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c2,multiply(sk_c1,X0))
| ~ spl0_17 ),
inference(superposition,[],[f4,f215]) ).
fof(f245,plain,
( ! [X0] : multiply(sk_c2,multiply(sk_c1,X0)) = X0
| ~ spl0_17 ),
inference(forward_demodulation,[],[f244,f1]) ).
fof(f248,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c7,X0))
| ~ spl0_8 ),
inference(superposition,[],[f4,f217]) ).
fof(f249,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c7,X0)) = X0
| ~ spl0_8 ),
inference(forward_demodulation,[],[f248,f1]) ).
fof(f257,plain,
( sk_c2 = multiply(sk_c2,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f245,f196]) ).
fof(f266,plain,
( multiply(sk_c1,sk_c2) = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f232,f257]) ).
fof(f268,plain,
( sk_c10 = multiply(sk_c10,sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f266,f196]) ).
fof(f284,definition,
( spl0_21
<=> sk_c9 = inverse(identity) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f285,plain,
( sk_c9 = inverse(identity)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
( sk_c9 != inverse(identity)
| spl0_21 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f295,plain,
( sk_c8 = multiply(sk_c8,sk_c9)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f249,f127]) ).
fof(f397,plain,
( sk_c10 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f241,f268]) ).
fof(f409,plain,
( sk_c9 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f241,f295]) ).
fof(f411,plain,
( sk_c10 = multiply(inverse(sk_c3),sk_c4)
| ~ spl0_14 ),
inference(superposition,[],[f241,f152]) ).
fof(f413,plain,
( ! [X0] :
( sk_c10 != sk_c9
| sk_c9 != inverse(multiply(inverse(X0),X0)) )
| ~ spl0_2 ),
inference(superposition,[],[f240,f241]) ).
fof(f416,plain,
( sk_c9 != inverse(identity)
| sk_c10 != sk_c9
| ~ spl0_2 ),
inference(forward_demodulation,[],[f413,f3]) ).
fof(f418,plain,
( sk_c10 = multiply(sk_c10,sk_c4)
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f411,f117]) ).
fof(f419,plain,
( identity = sk_c9
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f409,f3]) ).
fof(f422,plain,
( identity = sk_c10
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f397,f3]) ).
fof(f430,plain,
( spl0_20
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f422,f194,f183,f225]) ).
fof(f433,plain,
( sk_c9 = multiply(identity,sk_c4)
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f163,f226]) ).
fof(f435,plain,
( identity = multiply(identity,sk_c3)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f218,f226]) ).
fof(f446,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f435,f1]) ).
fof(f448,plain,
( sk_c9 = sk_c4
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f433,f1]) ).
fof(f451,plain,
( sk_c4 = multiply(identity,sk_c10)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(superposition,[],[f152,f446]) ).
fof(f452,plain,
( sk_c10 = inverse(identity)
| ~ spl0_7
| ~ spl0_20 ),
inference(superposition,[],[f117,f446]) ).
fof(f453,plain,
( identity = inverse(identity)
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f452,f226]) ).
fof(f454,plain,
( sk_c10 = sk_c4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f451,f1]) ).
fof(f457,plain,
( identity = sk_c4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_20 ),
inference(forward_demodulation,[],[f454,f226]) ).
fof(f485,plain,
( sk_c10 = multiply(sk_c10,sk_c9)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f418,f448]) ).
fof(f486,plain,
( identity = multiply(identity,sk_c9)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f485,f226]) ).
fof(f487,plain,
( identity = sk_c9
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f486,f1]) ).
fof(f612,plain,
( identity != sk_c9
| sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_20 ),
inference(forward_demodulation,[],[f416,f453]) ).
fof(f619,plain,
( sk_c10 != sk_c9
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f612,f487]) ).
fof(f626,plain,
( identity != sk_c10
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f619,f487]) ).
fof(f631,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f626,f226]) ).
fof(f632,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f631]) ).
fof(f633,plain,
( ! [X3] :
( sk_c9 != multiply(identity,multiply(X3,identity))
| sk_c10 != inverse(X3) )
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f105,f226]) ).
fof(f637,plain,
( ! [X3] :
( sk_c9 != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_4
| ~ spl0_20 ),
inference(forward_demodulation,[],[f633,f1]) ).
fof(f640,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f637,f487]) ).
fof(f641,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f640,f226]) ).
fof(f648,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f641,f3]) ).
fof(f652,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f648]) ).
fof(f655,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f652,f453]) ).
fof(f659,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f655,f453]) ).
fof(f660,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f664,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c10 != multiply(X4,sk_c9) )
| ~ spl0_3
| ~ spl0_20 ),
inference(forward_demodulation,[],[f102,f226]) ).
fof(f665,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f664,f487]) ).
fof(f666,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f665,f226]) ).
fof(f669,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f666,f3]) ).
fof(f673,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f669]) ).
fof(f676,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f673,f453]) ).
fof(f680,plain,
( $false
| ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f676,f453]) ).
fof(f681,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f680]) ).
fof(f685,plain,
( ! [X6] :
( identity != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f96,f487]) ).
fof(f686,plain,
( ! [X6] :
( sk_c9 != multiply(inverse(X6),identity)
| identity != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f685,f226]) ).
fof(f687,plain,
( ! [X6] :
( identity != multiply(inverse(X6),identity)
| identity != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f686,f487]) ).
fof(f693,plain,
( identity != multiply(sk_c10,identity)
| identity != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f687,f117]) ).
fof(f700,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f693,f226]) ).
fof(f708,plain,
( identity != multiply(sk_c3,sk_c10)
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f700,f1]) ).
fof(f712,plain,
( identity != sk_c4
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f708,f152]) ).
fof(f717,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f712,f457]) ).
fof(f718,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f717]) ).
fof(f723,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| sk_c10 != multiply(inverse(X0),sk_c9) )
| ~ spl0_5
| ~ spl0_20 ),
inference(forward_demodulation,[],[f108,f226]) ).
fof(f724,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f723,f487]) ).
fof(f725,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f724,f226]) ).
fof(f732,plain,
( identity != multiply(sk_c10,identity)
| identity != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(superposition,[],[f725,f117]) ).
fof(f739,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f732,f226]) ).
fof(f747,plain,
( identity != multiply(sk_c3,sk_c10)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f739,f1]) ).
fof(f751,plain,
( identity != sk_c4
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f747,f152]) ).
fof(f756,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f751,f457]) ).
fof(f757,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f756]) ).
fof(f763,plain,
( identity = inverse(sk_c5)
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f147,f226]) ).
fof(f766,plain,
( sk_c9 != multiply(sk_c10,identity)
| ~ spl0_7
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f162,f457]) ).
fof(f769,plain,
( identity = multiply(sk_c5,sk_c9)
| ~ spl0_12
| ~ spl0_20 ),
inference(forward_demodulation,[],[f142,f226]) ).
fof(f772,plain,
( sk_c9 != multiply(identity,identity)
| ~ spl0_7
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f766,f226]) ).
fof(f774,plain,
( identity != sk_c9
| ~ spl0_7
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(forward_demodulation,[],[f772,f1]) ).
fof(f776,plain,
( identity = multiply(sk_c9,sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f3,f132]) ).
fof(f781,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f3,f763]) ).
fof(f782,plain,
( identity = sk_c5
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f781,f1]) ).
fof(f787,plain,
( sk_c9 = multiply(inverse(sk_c5),identity)
| ~ spl0_12
| ~ spl0_20 ),
inference(superposition,[],[f241,f769]) ).
fof(f790,plain,
( sk_c9 = multiply(identity,identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f787,f763]) ).
fof(f791,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f790,f1]) ).
fof(f792,plain,
( $false
| ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f791,f774]) ).
fof(f793,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f792]) ).
fof(f811,plain,
( identity != inverse(identity)
| ~ spl0_8
| ~ spl0_9
| spl0_21 ),
inference(forward_demodulation,[],[f286,f419]) ).
fof(f813,plain,
( ! [X6] :
( identity != multiply(X6,inverse(X6))
| sk_c9 != multiply(inverse(X6),sk_c10) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f96,f419]) ).
fof(f814,plain,
( ! [X6] :
( identity != multiply(inverse(X6),sk_c10)
| identity != multiply(X6,inverse(X6)) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f813,f419]) ).
fof(f822,plain,
( identity != multiply(sk_c8,sk_c10)
| identity != multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f814,f122]) ).
fof(f829,plain,
( identity != sk_c9
| identity != multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f822,f113]) ).
fof(f854,plain,
( identity != multiply(sk_c7,sk_c8)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f829,f419]) ).
fof(f856,plain,
( identity != sk_c9
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_demodulation,[],[f854,f127]) ).
fof(f857,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f856,f419]) ).
fof(f858,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f897,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f776,f419]) ).
fof(f898,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f897,f1]) ).
fof(f899,plain,
( sk_c9 = inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f132,f898]) ).
fof(f901,plain,
( sk_c10 = multiply(identity,sk_c9)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f137,f898]) ).
fof(f902,plain,
( sk_c10 = sk_c9
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f901,f1]) ).
fof(f904,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f899,f419]) ).
fof(f908,plain,
( $false
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f904,f811]) ).
fof(f909,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_21 ),
inference(avatar_contradiction_clause,[],[f908]) ).
fof(f911,plain,
( identity = inverse(identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_21 ),
inference(forward_demodulation,[],[f285,f419]) ).
fof(f913,plain,
( identity = sk_c10
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f902,f419]) ).
fof(f919,plain,
( ! [X4] :
( sk_c10 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f664,f419]) ).
fof(f932,plain,
( spl0_20
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f913,f135,f130,f125,f120,f225]) ).
fof(f948,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f919,f226]) ).
fof(f954,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f948,f3]) ).
fof(f955,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f954]) ).
fof(f957,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f955,f911]) ).
fof(f960,plain,
( $false
| ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f957,f911]) ).
fof(f961,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f960]) ).
fof(f963,plain,
( ! [X0] :
( sk_c10 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f723,f419]) ).
fof(f965,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f963,f226]) ).
fof(f972,plain,
( identity != multiply(sk_c10,identity)
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[],[f965,f147]) ).
fof(f981,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f972,f226]) ).
fof(f988,plain,
( identity != multiply(sk_c5,sk_c10)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f981,f1]) ).
fof(f990,plain,
( identity != multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f988,f226]) ).
fof(f993,plain,
( identity != multiply(identity,identity)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_demodulation,[],[f990,f782]) ).
fof(f994,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[],[f993,f1]) ).
fof(f995,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f994]) ).
fof(f997,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c10 != inverse(X3) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f637,f419]) ).
fof(f999,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(forward_demodulation,[],[f997,f226]) ).
fof(f1004,plain,
( identity != identity
| identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(superposition,[],[f999,f3]) ).
fof(f1005,plain,
( identity != inverse(inverse(identity))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f1004]) ).
fof(f1007,plain,
( identity != inverse(identity)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_demodulation,[],[f1005,f911]) ).
fof(f1010,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f1007,f911]) ).
fof(f1011,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f1010]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f109]) ).
cnf(s2,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f118]) ).
cnf(s3,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f123]) ).
cnf(s4,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f128]) ).
cnf(s5,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f133]) ).
cnf(s6,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f148]) ).
cnf(s9,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s10,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s11,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s12,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s13,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f157]) ).
cnf(s15,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f159]) ).
cnf(s21,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f169]) ).
cnf(s22,plain,
( spl0_13
| spl0_15 ),
inference(sat_conversion,[],[f170]) ).
cnf(s31,plain,
( spl0_8
| spl0_17 ),
inference(sat_conversion,[],[f187]) ).
cnf(s32,plain,
( spl0_9
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s33,plain,
( spl0_10
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s34,plain,
( spl0_11
| spl0_17 ),
inference(sat_conversion,[],[f190]) ).
cnf(s38,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s39,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s40,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s41,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f201]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f211]) ).
cnf(s53,plain,
( ~ spl0_17
| ~ spl0_18
| spl0_20 ),
inference(sat_conversion,[],[f430]) ).
cnf(s62,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f632]) ).
cnf(s64,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f660]) ).
cnf(s67,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f681]) ).
cnf(s72,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f718]) ).
cnf(s78,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f757]) ).
cnf(s83,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| spl0_15
| ~ spl0_20 ),
inference(sat_conversion,[],[f793]) ).
cnf(s87,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f858]) ).
cnf(s92,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_21 ),
inference(sat_conversion,[],[f909]) ).
cnf(s98,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| spl0_20 ),
inference(sat_conversion,[],[f932]) ).
cnf(s100,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f961]) ).
cnf(s105,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13
| ~ spl0_20 ),
inference(sat_conversion,[],[f995]) ).
cnf(s107,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f1011]) ).
cnf(s109,plain,
( spl0_18
| spl0_20 ),
inference(rat,[],[s98,s38,s39,s40,s41]) ).
cnf(s110,plain,
( ~ spl0_18
| spl0_20 ),
inference(rat,[],[s98,s31,s32,s33,s34,s53]) ).
cnf(s111,plain,
spl0_20,
inference(rat,[],[s110,s109]) ).
cnf(s112,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_7 ),
inference(rat,[],[s83,s21,s22,s78,s111]) ).
cnf(s113,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s105,s10,s11,s15,s111]) ).
cnf(s114,plain,
( ~ spl0_5
| ~ spl0_14 ),
inference(rat,[],[s105,s3,s4,s8,s112,s111]) ).
cnf(s115,plain,
~ spl0_5,
inference(rat,[],[s114,s113]) ).
cnf(s116,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s83,s21,s22,s64,s111]) ).
cnf(s117,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s92,s107,s10,s11,s12,s111]) ).
cnf(s118,plain,
( ~ spl0_14
| ~ spl0_4 ),
inference(rat,[],[s92,s107,s3,s4,s5,s116,s111]) ).
cnf(s119,plain,
~ spl0_4,
inference(rat,[],[s118,s117]) ).
cnf(s120,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s83,s21,s22,s67,s111]) ).
cnf(s121,plain,
( spl0_14
| ~ spl0_3 ),
inference(rat,[],[s92,s100,s10,s11,s12,s111]) ).
cnf(s122,plain,
( ~ spl0_14
| ~ spl0_3 ),
inference(rat,[],[s92,s100,s3,s4,s5,s120,s111]) ).
cnf(s123,plain,
~ spl0_3,
inference(rat,[],[s122,s121]) ).
cnf(s124,plain,
( ~ spl0_14
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s83,s21,s22,s62,s111]) ).
cnf(s125,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s45,s12,s13]) ).
cnf(s126,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s45,s5,s6,s124]) ).
cnf(s127,plain,
~ spl0_2,
inference(rat,[],[s126,s125]) ).
cnf(s128,plain,
spl0_1,
inference(rat,[],[s1,s115,s119,s123,s127]) ).
cnf(s129,plain,
( ~ spl0_14
| ~ spl0_7 ),
inference(rat,[],[s83,s21,s22,s72,s128,s111]) ).
cnf(s130,plain,
spl0_14,
inference(rat,[],[s87,s9,s10,s11,s128]) ).
cnf(s131,plain,
~ spl0_7,
inference(rat,[],[s129,s130]) ).
cnf(s136,plain,
spl0_9,
inference(rat,[],[s4,s131]) ).
cnf(s137,plain,
spl0_8,
inference(rat,[],[s3,s131]) ).
cnf(s138,plain,
spl0_6,
inference(rat,[],[s2,s131]) ).
cnf(s141,plain,
$false,
inference(rat,[],[s87,s136,s128,s137,s138]) ).
fof(f1012,plain,
$false,
inference(avatar_sat_refutation,[],[s141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP209-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.22/0.46 % Computer : n016.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Sun Sep 27 09:42:31 UTC 2026
% 0.22/0.46 % CPUTime :
% 0.22/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.51 Running first-order model finding
% 0.26/0.51 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
% 0.65/0.61 % (2375113)Will run a generic schedule for satisfiability detection.
% 0.65/0.61 % (2375124)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=495096248:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.65/0.61 % (2375119)% WARNING: option uhcvi not known.
% 0.65/0.61 % (2375123)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1540288618:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.65/0.61 % (2375119)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=652363739:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.65/0.61 % (2375118)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3779087115_2999 on theBenchmark for (2999ds/0Mi)
% 0.65/0.61 % (2375120)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3976787986:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.65/0.61 % (2375121)dis+10_1_sil=32000:sp=arity:random_seed=3428783650:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.65/0.61 % (2375122)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=272202:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.65/0.61 % TRYING [1]
% 0.65/0.61 % TRYING [2]
% 0.65/0.61 % TRYING [3]
% 0.65/0.61 % TRYING [4]
% 0.65/0.61 % (2375121) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2375113-2375121"...
% 0.65/0.61 % (2375122) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2375113-2375122"...
% 0.65/0.61 % (2375121)...printing done.
% 0.65/0.61 % (2375124) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2375113-2375124"...
% 0.65/0.61 % (2375119) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2375113-2375119"...
% 0.65/0.61 % (2375121)Refutation found. Thanks to Tanya!
% 0.65/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.65/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.65/0.62 % (2375121)------------------------------
% 0.65/0.62 % (2375121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.65/0.62 % (2375121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.65/0.62 % (2375121)CaDiCaL version: 2.1.3
% 0.65/0.62 % (2375121)Termination reason: Refutation
% 0.65/0.62 % (2375121)Time elapsed: 0.034 s
% 0.65/0.62 % (2375121)Peak memory usage: 12 MB
% 0.65/0.62 % (2375121)Instructions burned: 32 (million)
% 0.65/0.62 % (2375113)Success in time 0.09 s
% 0.65/0.62 % Vampire exiting
%------------------------------------------------------------------------------