%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP251-1 : 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 : n020.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 10:17:17 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 52
% Syntax : Number of formulae : 339 ( 21 unt; 18 def)
% Number of atoms : 1245 ( 367 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1766 ( 860 ~; 888 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 95 !; 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(f5,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c10) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c1) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c1)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c10
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c10 = inverse(sk_c1)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f37,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c9) = sk_c8
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f45]) ).
fof(f51,negated_conjecture,
( inverse(sk_c2) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c2)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f53]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = inverse(sk_c2)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = inverse(sk_c3)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c5,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c5) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c9,sk_c7) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| multiply(sk_c6,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c9
| inverse(sk_c6) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f88,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| sk_c9 = inverse(sk_c6) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X0,sk_c10) != sk_c9
| inverse(X0) != sk_c10
| multiply(X1,sk_c9) != sk_c8
| inverse(X1) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| multiply(X3,sk_c10) != sk_c9
| inverse(X3) != sk_c10
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c8
| multiply(sk_c9,X5) != sk_c8
| multiply(X6,sk_c9) != X5
| inverse(X6) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X0,sk_c10)
| inverse(X0) != sk_c10
| sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1)
| sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8)
| sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4)
| sk_c8 != multiply(sk_c9,X5)
| multiply(X6,sk_c9) != X5
| sk_c9 != inverse(X6) ),
inference(reorient_equations,[],[f89]) ).
fof(f92,definition,
( spl0_1
<=> ! [X6,X5] :
( sk_c8 != multiply(sk_c9,X5)
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f93,plain,
( ! [X6,X5] :
( sk_c8 != multiply(sk_c9,X5)
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f92]) ).
fof(f95,definition,
( spl0_2
<=> ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f96,plain,
( ! [X4] :
( sk_c9 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f98,definition,
( spl0_3
<=> ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f99,plain,
( ! [X3] :
( sk_c9 != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,definition,
( spl0_4
<=> ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f102,plain,
( ! [X2] :
( sk_c9 != inverse(X2)
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f104,definition,
( spl0_5
<=> ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f105,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c9)
| sk_c9 != inverse(X1) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f90,f98,f104,f101,f98,f95,f92]) ).
fof(f108,definition,
( spl0_6
<=> sk_c9 = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f110,plain,
( sk_c9 = inverse(sk_c6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f112,definition,
( spl0_7
<=> sk_c9 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f114,plain,
( sk_c9 = multiply(sk_c3,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f115,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f88,f112,f108]) ).
fof(f117,definition,
( spl0_8
<=> sk_c7 = multiply(sk_c6,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f119,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f120,plain,
( spl0_8
| spl0_7 ),
inference(avatar_split_clause,[],[f86,f112,f117]) ).
fof(f122,definition,
( spl0_9
<=> sk_c8 = multiply(sk_c9,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f124,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f125,plain,
( spl0_9
| spl0_7 ),
inference(avatar_split_clause,[],[f84,f112,f122]) ).
fof(f127,definition,
( spl0_10
<=> sk_c8 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f129,plain,
( sk_c8 = inverse(sk_c5)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f130,plain,
( spl0_10
| spl0_7 ),
inference(avatar_split_clause,[],[f82,f112,f127]) ).
fof(f132,definition,
( spl0_11
<=> sk_c9 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f134,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f132]) ).
fof(f135,plain,
( spl0_11
| spl0_7 ),
inference(avatar_split_clause,[],[f80,f112,f132]) ).
fof(f137,definition,
( spl0_12
<=> sk_c10 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f139,plain,
( sk_c10 = inverse(sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl0_12
| spl0_7 ),
inference(avatar_split_clause,[],[f78,f112,f137]) ).
fof(f142,definition,
( spl0_13
<=> sk_c9 = multiply(sk_c4,sk_c10) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f144,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_13
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f112,f142]) ).
fof(f147,definition,
( spl0_14
<=> sk_c9 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f149,plain,
( sk_c9 = inverse(sk_c3)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f150,plain,
( spl0_6
| spl0_14 ),
inference(avatar_split_clause,[],[f74,f147,f108]) ).
fof(f151,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f72,f147,f117]) ).
fof(f152,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f70,f147,f122]) ).
fof(f153,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f68,f147,f127]) ).
fof(f154,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f66,f147,f132]) ).
fof(f155,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f64,f147,f137]) ).
fof(f156,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f62,f147,f142]) ).
fof(f158,definition,
( spl0_15
<=> sk_c9 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f160,plain,
( sk_c9 = inverse(sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f161,plain,
( spl0_6
| spl0_15 ),
inference(avatar_split_clause,[],[f60,f158,f108]) ).
fof(f164,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f54,f158,f127]) ).
fof(f165,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f52,f158,f132]) ).
fof(f169,definition,
( spl0_16
<=> sk_c8 = multiply(sk_c2,sk_c9) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f171,plain,
( sk_c8 = multiply(sk_c2,sk_c9)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
( spl0_6
| spl0_16 ),
inference(avatar_split_clause,[],[f46,f169,f108]) ).
fof(f175,plain,
( spl0_10
| spl0_16 ),
inference(avatar_split_clause,[],[f40,f169,f127]) ).
fof(f176,plain,
( spl0_11
| spl0_16 ),
inference(avatar_split_clause,[],[f38,f169,f132]) ).
fof(f180,definition,
( spl0_17
<=> sk_c10 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f181,plain,
( sk_c10 != inverse(sk_c1)
| spl0_17 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f182,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl0_6
| spl0_17 ),
inference(avatar_split_clause,[],[f32,f180,f108]) ).
fof(f188,plain,
( spl0_12
| spl0_17 ),
inference(avatar_split_clause,[],[f22,f180,f137]) ).
fof(f189,plain,
( spl0_13
| spl0_17 ),
inference(avatar_split_clause,[],[f20,f180,f142]) ).
fof(f191,definition,
( spl0_18
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f193,plain,
( multiply(sk_c1,sk_c10) = sk_c9
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl0_6
| spl0_18 ),
inference(avatar_split_clause,[],[f18,f191,f108]) ).
fof(f195,plain,
( spl0_8
| spl0_18 ),
inference(avatar_split_clause,[],[f16,f191,f117]) ).
fof(f196,plain,
( spl0_9
| spl0_18 ),
inference(avatar_split_clause,[],[f14,f191,f122]) ).
fof(f197,plain,
( spl0_10
| spl0_18 ),
inference(avatar_split_clause,[],[f12,f191,f127]) ).
fof(f198,plain,
( spl0_11
| spl0_18 ),
inference(avatar_split_clause,[],[f10,f191,f132]) ).
fof(f199,plain,
( spl0_12
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f191,f137]) ).
fof(f200,plain,
( spl0_13
| spl0_18 ),
inference(avatar_split_clause,[],[f6,f191,f142]) ).
fof(f201,plain,
( sk_c9 = multiply(sk_c5,inverse(sk_c5))
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f134,f129]) ).
fof(f202,plain,
( ! [X0] :
( sk_c9 != multiply(X0,inverse(sk_c5))
| inverse(X0) != inverse(sk_c5) )
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f96,f129]) ).
fof(f203,plain,
( sk_c9 != sk_c9
| inverse(sk_c5) != inverse(sk_c5)
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f202,f201]) ).
fof(f204,plain,
( $false
| ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f203]) ).
fof(f205,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f204]) ).
fof(f206,plain,
( sk_c9 = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f193,f182]) ).
fof(f209,plain,
( sk_c9 != sk_c9
| sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f96,f114]) ).
fof(f210,plain,
( sk_c8 != inverse(sk_c3)
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f209]) ).
fof(f211,plain,
( sk_c9 != sk_c8
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[],[f210,f149]) ).
fof(f212,plain,
( sk_c8 != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f211,f206]) ).
fof(f215,plain,
( sk_c8 = multiply(sk_c2,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f171,f206]) ).
fof(f221,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[],[f3,f3]) ).
fof(f222,plain,
( identity = multiply(sk_c10,sk_c4)
| ~ spl0_12 ),
inference(superposition,[],[f3,f139]) ).
fof(f225,plain,
( identity = multiply(sk_c9,sk_c3)
| ~ spl0_14 ),
inference(superposition,[],[f3,f149]) ).
fof(f226,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(superposition,[],[f1,f3]) ).
fof(f229,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f226,f4]) ).
fof(f230,plain,
( identity = multiply(multiply(sk_c1,inverse(sk_c1)),sk_c3)
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f225,f206]) ).
fof(f243,plain,
( identity = multiply(sk_c1,multiply(inverse(sk_c1),sk_c3))
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f230,f4]) ).
fof(f281,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(multiply(inverse(sk_c1),sk_c3),X0))
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f4,f243]) ).
fof(f282,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c3,X0)))
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f281,f4]) ).
fof(f283,plain,
( ! [X0] : multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c3,X0))) = X0
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f282,f1]) ).
fof(f302,plain,
( sk_c8 = multiply(sk_c1,multiply(inverse(sk_c1),sk_c9))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f283,f114]) ).
fof(f307,plain,
( sk_c8 = multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c1,inverse(sk_c1))))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f302,f206]) ).
fof(f309,plain,
( sk_c8 = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f307,f229]) ).
fof(f310,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f309,f212]) ).
fof(f311,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f310]) ).
fof(f312,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c1,inverse(sk_c1))
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f102,f206]) ).
fof(f313,plain,
( ! [X2] :
( sk_c9 != multiply(X2,multiply(sk_c1,inverse(sk_c1)))
| inverse(X2) != multiply(sk_c1,inverse(sk_c1)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f312,f309]) ).
fof(f314,plain,
( ! [X2] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X2,multiply(sk_c1,inverse(sk_c1)))
| inverse(X2) != multiply(sk_c1,inverse(sk_c1)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f313,f206]) ).
fof(f319,plain,
( sk_c8 != multiply(sk_c1,inverse(sk_c1))
| inverse(sk_c2) != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f314,f215]) ).
fof(f321,plain,
( inverse(sk_c2) != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f319,f309]) ).
fof(f328,plain,
( sk_c9 != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f321,f160]) ).
fof(f330,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f328,f206]) ).
fof(f331,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f330]) ).
fof(f332,plain,
( ! [X1] :
( sk_c8 != multiply(X1,multiply(sk_c1,inverse(sk_c1)))
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f105,f206]) ).
fof(f333,plain,
( ! [X1] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X1,multiply(sk_c1,inverse(sk_c1)))
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f332,f309]) ).
fof(f334,plain,
( ! [X1] :
( inverse(X1) != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(X1,multiply(sk_c1,inverse(sk_c1))) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f333,f206]) ).
fof(f335,plain,
( sk_c9 = multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f114,f309]) ).
fof(f340,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f335,f206]) ).
fof(f343,plain,
( sk_c9 != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c2,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f334,f160]) ).
fof(f344,plain,
( sk_c9 != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f334,f149]) ).
fof(f345,plain,
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f344,f206]) ).
fof(f346,plain,
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c2,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f343,f206]) ).
fof(f349,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f345,f340]) ).
fof(f350,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f351,plain,
( sk_c8 != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f346,f215]) ).
fof(f362,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f351,f309]) ).
fof(f363,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f364,plain,
( ! [X3] :
( sk_c9 != multiply(X3,inverse(sk_c1))
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f99,f182]) ).
fof(f365,plain,
( ! [X3] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X3,inverse(sk_c1))
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f364,f206]) ).
fof(f366,plain,
( ! [X3] :
( inverse(sk_c1) != inverse(X3)
| multiply(sk_c1,inverse(sk_c1)) != multiply(X3,inverse(sk_c1)) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f365,f182]) ).
fof(f379,plain,
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(equality_resolution,[],[f366]) ).
fof(f380,plain,
( $false
| ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f379]) ).
fof(f381,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f380]) ).
fof(f403,plain,
( ! [X6,X5] :
( sk_c8 != multiply(multiply(sk_c1,inverse(sk_c1)),X5)
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f93,f206]) ).
fof(f404,plain,
( ! [X6,X5] :
( sk_c8 != multiply(sk_c1,multiply(inverse(sk_c1),X5))
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f403,f4]) ).
fof(f405,plain,
( ! [X6,X5] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),X5))
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f404,f309]) ).
fof(f406,plain,
( ! [X6,X5] :
( inverse(X6) != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),X5))
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f405,f206]) ).
fof(f407,plain,
( ! [X6,X5] :
( multiply(X6,multiply(sk_c1,inverse(sk_c1))) != X5
| inverse(X6) != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),X5)) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f406,f206]) ).
fof(f419,plain,
( ! [X0] :
( inverse(X0) != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),multiply(X0,multiply(sk_c1,inverse(sk_c1))))) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(equality_resolution,[],[f407]) ).
fof(f658,plain,
( sk_c9 != multiply(sk_c1,inverse(sk_c1))
| multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f419,f149]) ).
fof(f664,plain,
( inverse(sk_c5) = multiply(sk_c1,inverse(sk_c1))
| ~ spl0_7
| ~ spl0_10
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f129,f309]) ).
fof(f665,plain,
( sk_c9 = multiply(sk_c5,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_7
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f134,f309]) ).
fof(f668,plain,
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,multiply(inverse(sk_c1),multiply(sk_c3,multiply(sk_c1,inverse(sk_c1)))))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f658,f206]) ).
fof(f671,plain,
( multiply(sk_c1,inverse(sk_c1)) = multiply(sk_c5,multiply(sk_c1,inverse(sk_c1)))
| ~ spl0_7
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f665,f206]) ).
fof(f678,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f668,f283]) ).
fof(f679,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f678]) ).
fof(f688,plain,
( ! [X2] :
( inverse(X2) != multiply(sk_c1,inverse(sk_c1))
| sk_c9 != multiply(X2,sk_c8) )
| ~ spl0_4
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f102,f206]) ).
fof(f689,plain,
( ! [X2] :
( sk_c9 != multiply(X2,multiply(sk_c1,inverse(sk_c1)))
| inverse(X2) != multiply(sk_c1,inverse(sk_c1)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f688,f309]) ).
fof(f690,plain,
( ! [X2] :
( multiply(sk_c1,inverse(sk_c1)) != multiply(X2,multiply(sk_c1,inverse(sk_c1)))
| inverse(X2) != multiply(sk_c1,inverse(sk_c1)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[],[f689,f206]) ).
fof(f715,plain,
( multiply(sk_c1,inverse(sk_c1)) != multiply(sk_c1,inverse(sk_c1))
| inverse(sk_c5) != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f690,f671]) ).
fof(f718,plain,
( inverse(sk_c5) != multiply(sk_c1,inverse(sk_c1))
| ~ spl0_4
| ~ spl0_7
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f715]) ).
fof(f722,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f718,f664]) ).
fof(f723,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f722]) ).
fof(f878,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f229,f3]) ).
fof(f880,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f229,f229]) ).
fof(f938,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f878,f880]) ).
fof(f1252,plain,
( ! [X2] :
( sk_c9 != multiply(X2,inverse(sk_c5))
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10 ),
inference(forward_demodulation,[],[f102,f129]) ).
fof(f1292,plain,
( sk_c4 = multiply(inverse(sk_c10),identity)
| ~ spl0_12 ),
inference(superposition,[],[f229,f222]) ).
fof(f1295,plain,
( sk_c4 = inverse(sk_c10)
| ~ spl0_12 ),
inference(forward_demodulation,[],[f1292,f938]) ).
fof(f1304,plain,
( sk_c10 = inverse(inverse(sk_c10))
| ~ spl0_12 ),
inference(superposition,[],[f139,f1295]) ).
fof(f1305,plain,
( sk_c9 = multiply(inverse(sk_c10),sk_c10)
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f144,f1295]) ).
fof(f1307,plain,
( identity = sk_c9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1305,f3]) ).
fof(f1309,plain,
( identity = multiply(sk_c1,sk_c10)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f193,f1307]) ).
fof(f1310,plain,
( sk_c8 = multiply(identity,sk_c7)
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f124,f1307]) ).
fof(f1311,plain,
( sk_c8 = sk_c7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1310,f1]) ).
fof(f1345,plain,
( sk_c10 = multiply(inverse(sk_c1),identity)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[],[f229,f1309]) ).
fof(f1348,plain,
( sk_c10 = inverse(sk_c1)
| ~ spl0_12
| ~ spl0_13
| ~ spl0_18 ),
inference(forward_demodulation,[],[f1345,f938]) ).
fof(f1350,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f1348,f181]) ).
fof(f1351,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f1350]) ).
fof(f1358,plain,
( identity = inverse(sk_c6)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f110,f1307]) ).
fof(f1359,plain,
( sk_c7 = multiply(sk_c6,identity)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f119,f1307]) ).
fof(f1366,plain,
( ! [X2] :
( identity != multiply(X2,inverse(sk_c5))
| sk_c9 != inverse(X2) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1252,f1307]) ).
fof(f1368,plain,
( inverse(sk_c5) = sk_c7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1311,f129]) ).
fof(f1371,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1359,f938]) ).
fof(f1377,plain,
( ! [X2] :
( identity != inverse(X2)
| identity != multiply(X2,inverse(sk_c5)) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1366,f1307]) ).
fof(f1380,plain,
( inverse(sk_c5) = sk_c6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1371,f1368]) ).
fof(f1385,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f1358]) ).
fof(f1386,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1385,f1]) ).
fof(f1393,plain,
( identity = inverse(inverse(sk_c5))
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1358,f1380]) ).
fof(f1395,plain,
( identity = inverse(sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1380,f1386]) ).
fof(f1401,plain,
( identity = multiply(identity,sk_c5)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f3,f1395]) ).
fof(f1402,plain,
( identity = sk_c5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1401,f1]) ).
fof(f1426,plain,
( identity != identity
| identity != multiply(sk_c6,inverse(sk_c5))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1377,f1358]) ).
fof(f1428,plain,
( identity != multiply(sk_c6,inverse(sk_c5))
| ~ spl0_4
| ~ spl0_6
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1426]) ).
fof(f1432,plain,
( identity != multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1428,f1395]) ).
fof(f1439,plain,
( identity != sk_c6
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1432,f938]) ).
fof(f1448,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1439,f1386]) ).
fof(f1449,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1448]) ).
fof(f1463,plain,
( ! [X1] :
( sk_c8 != multiply(X1,identity)
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f105,f1307]) ).
fof(f1464,plain,
( ! [X1] :
( sk_c8 != X1
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1463,f938]) ).
fof(f1465,plain,
( ! [X1] :
( inverse(sk_c5) != X1
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1464,f129]) ).
fof(f1466,plain,
( ! [X1] :
( identity != X1
| sk_c9 != inverse(X1) )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1465,f1395]) ).
fof(f1467,plain,
( ! [X1] :
( identity != inverse(X1)
| identity != X1 )
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1466,f1307]) ).
fof(f1476,plain,
( identity != identity
| identity != sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1467,f1395]) ).
fof(f1480,plain,
( identity != sk_c5
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1476]) ).
fof(f1487,plain,
( $false
| ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1480,f1402]) ).
fof(f1488,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1487]) ).
fof(f1492,plain,
( ! [X6,X5] :
( sk_c8 != multiply(identity,X5)
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f93,f1307]) ).
fof(f1493,plain,
( ! [X6,X5] :
( sk_c8 != X5
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1492,f1]) ).
fof(f1494,plain,
( ! [X6,X5] :
( inverse(sk_c5) != X5
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1493,f129]) ).
fof(f1495,plain,
( ! [X6,X5] :
( identity != X5
| sk_c9 != inverse(X6)
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1494,f1395]) ).
fof(f1496,plain,
( ! [X6,X5] :
( identity != inverse(X6)
| identity != X5
| multiply(X6,sk_c9) != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1495,f1307]) ).
fof(f1497,plain,
( ! [X6,X5] :
( multiply(X6,identity) != X5
| identity != inverse(X6)
| identity != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1496,f1307]) ).
fof(f1498,plain,
( ! [X6,X5] :
( X5 != X6
| identity != inverse(X6)
| identity != X5 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f1497,f938]) ).
fof(f1501,plain,
( ! [X0] :
( identity != inverse(X0)
| identity != X0 )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(equality_resolution,[],[f1498]) ).
fof(f1518,plain,
( identity != identity
| identity != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1501,f1393]) ).
fof(f1525,plain,
( identity != inverse(sk_c5)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f1518]) ).
fof(f1535,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1525,f1395]) ).
fof(f1536,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1535]) ).
fof(f1539,plain,
( ! [X3] :
( identity != multiply(X3,sk_c10)
| sk_c10 != inverse(X3) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f99,f1307]) ).
fof(f1561,plain,
( ! [X0] :
( identity != multiply(inverse(X0),X0)
| sk_c10 != inverse(inverse(sk_c10)) )
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f1539,f221]) ).
fof(f1570,plain,
( ! [X0] : identity != multiply(inverse(X0),X0)
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1561,f1304]) ).
fof(f1577,plain,
( $false
| ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1570,f3]) ).
fof(f1578,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f1577]) ).
cnf(s1,plain,
( spl0_3
| spl0_2
| spl0_1
| spl0_3
| spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f106]) ).
cnf(s2,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| spl0_5 ),
inference(rat,[],[s1]) ).
cnf(s3,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f115]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f120]) ).
cnf(s5,plain,
( spl0_7
| spl0_9 ),
inference(sat_conversion,[],[f125]) ).
cnf(s6,plain,
( spl0_7
| spl0_10 ),
inference(sat_conversion,[],[f130]) ).
cnf(s7,plain,
( spl0_7
| spl0_11 ),
inference(sat_conversion,[],[f135]) ).
cnf(s8,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f140]) ).
cnf(s9,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f145]) ).
cnf(s10,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f150]) ).
cnf(s11,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f151]) ).
cnf(s12,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f152]) ).
cnf(s13,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f153]) ).
cnf(s14,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f154]) ).
cnf(s15,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f155]) ).
cnf(s16,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f156]) ).
cnf(s17,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f161]) ).
cnf(s20,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f164]) ).
cnf(s21,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f165]) ).
cnf(s24,plain,
( spl0_6
| spl0_16 ),
inference(sat_conversion,[],[f172]) ).
cnf(s27,plain,
( spl0_10
| spl0_16 ),
inference(sat_conversion,[],[f175]) ).
cnf(s28,plain,
( spl0_11
| spl0_16 ),
inference(sat_conversion,[],[f176]) ).
cnf(s31,plain,
( spl0_6
| spl0_17 ),
inference(sat_conversion,[],[f183]) ).
cnf(s36,plain,
( spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f188]) ).
cnf(s37,plain,
( spl0_13
| spl0_17 ),
inference(sat_conversion,[],[f189]) ).
cnf(s38,plain,
( spl0_6
| spl0_18 ),
inference(sat_conversion,[],[f194]) ).
cnf(s39,plain,
( spl0_8
| spl0_18 ),
inference(sat_conversion,[],[f195]) ).
cnf(s40,plain,
( spl0_9
| spl0_18 ),
inference(sat_conversion,[],[f196]) ).
cnf(s41,plain,
( spl0_10
| spl0_18 ),
inference(sat_conversion,[],[f197]) ).
cnf(s42,plain,
( spl0_11
| spl0_18 ),
inference(sat_conversion,[],[f198]) ).
cnf(s43,plain,
( spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f199]) ).
cnf(s44,plain,
( spl0_13
| spl0_18 ),
inference(sat_conversion,[],[f200]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f205]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f311]) ).
cnf(s49,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f331]) ).
cnf(s51,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f350]) ).
cnf(s53,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_14
| ~ spl0_15
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f363]) ).
cnf(s54,plain,
( ~ spl0_3
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f381]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f679]) ).
cnf(s76,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_11
| ~ spl0_14
| ~ spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f723]) ).
cnf(s96,plain,
( ~ spl0_12
| ~ spl0_13
| spl0_17
| ~ spl0_18 ),
inference(sat_conversion,[],[f1351]) ).
cnf(s100,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1449]) ).
cnf(s106,plain,
( ~ spl0_5
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1488]) ).
cnf(s111,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1536]) ).
cnf(s116,plain,
( ~ spl0_3
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s118,plain,
( spl0_6
| ~ spl0_5 ),
inference(rat,[],[s53,s3,s10,s17,s24,s31,s38]) ).
cnf(s119,plain,
( spl0_18
| ~ spl0_5 ),
inference(rat,[],[s106,s39,s40,s41,s43,s44,s118]) ).
cnf(s120,plain,
( spl0_17
| ~ spl0_18 ),
inference(rat,[],[s96,s36,s37]) ).
cnf(s121,plain,
( spl0_14
| ~ spl0_5 ),
inference(rat,[],[s106,s11,s12,s13,s15,s16,s118]) ).
cnf(s122,plain,
~ spl0_5,
inference(rat,[],[s106,s4,s5,s6,s8,s9,s51,s121,s120,s119,s118]) ).
cnf(s123,plain,
( spl0_18
| ~ spl0_4 ),
inference(rat,[],[s100,s38,s39,s40,s41,s43,s44]) ).
cnf(s124,plain,
( spl0_10
| ~ spl0_17
| ~ spl0_14
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s49,s20,s27,s123]) ).
cnf(s125,plain,
( ~ spl0_10
| ~ spl0_17
| ~ spl0_4
| ~ spl0_7
| ~ spl0_14
| ~ spl0_18 ),
inference(rat,[],[s49,s21,s28,s76]) ).
cnf(s126,plain,
( ~ spl0_17
| ~ spl0_14
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s125,s124,s123]) ).
cnf(s127,plain,
( spl0_14
| ~ spl0_4 ),
inference(rat,[],[s100,s10,s11,s12,s13,s15,s16]) ).
cnf(s128,plain,
( ~ spl0_14
| ~ spl0_4
| ~ spl0_17 ),
inference(rat,[],[s100,s3,s4,s5,s6,s8,s9,s126]) ).
cnf(s129,plain,
~ spl0_4,
inference(rat,[],[s128,s127,s120,s123]) ).
cnf(s130,plain,
( spl0_18
| ~ spl0_3 ),
inference(rat,[],[s116,s43,s44]) ).
cnf(s131,plain,
~ spl0_3,
inference(rat,[],[s54,s120,s130]) ).
cnf(s132,plain,
( spl0_14
| ~ spl0_2 ),
inference(rat,[],[s45,s13,s14]) ).
cnf(s133,plain,
( spl0_7
| ~ spl0_2 ),
inference(rat,[],[s45,s6,s7]) ).
cnf(s134,plain,
( spl0_18
| ~ spl0_2 ),
inference(rat,[],[s45,s41,s42]) ).
cnf(s135,plain,
~ spl0_2,
inference(rat,[],[s47,s120,s134,s133,s132]) ).
cnf(s136,plain,
spl0_1,
inference(rat,[],[s2,s122,s129,s131,s135]) ).
cnf(s137,plain,
spl0_14,
inference(rat,[],[s111,s10,s11,s12,s13,s15,s16,s136]) ).
cnf(s138,plain,
spl0_7,
inference(rat,[],[s111,s3,s4,s5,s6,s8,s9,s136]) ).
cnf(s139,plain,
spl0_18,
inference(rat,[],[s111,s38,s39,s40,s41,s43,s44,s136]) ).
cnf(s140,plain,
spl0_17,
inference(rat,[],[s120,s139]) ).
cnf(s141,plain,
$false,
inference(rat,[],[s73,s137,s136,s138,s140,s139]) ).
fof(f1580,plain,
$false,
inference(avatar_sat_refutation,[],[s141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:43:49 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.15/0.40 Running first-order model finding
% 0.15/0.40 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
% 0.15/0.45 % (3143432)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (3143442)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1133647679:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.45 % (3143438)% WARNING: option uhcvi not known.
% 0.15/0.45 % (3143437)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=604898389_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.45 % (3143438)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3363233534:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.45 % (3143439)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3499619409:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.45 % (3143441)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4224140405:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.45 % (3143443)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2668528627:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (3143440)dis+10_1_sil=32000:sp=arity:random_seed=3674036492:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.45 % TRYING [1]
% 0.15/0.45 % TRYING [2]
% 0.15/0.45 % TRYING [3]
% 0.15/0.45 % (3143442) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3143432-3143442"...
% 0.15/0.45 % TRYING [4]
% 0.15/0.45 % (3143442)...printing done.
% 0.15/0.45 % (3143442)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (3143442)------------------------------
% 0.15/0.46 % (3143442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (3143442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (3143442)CaDiCaL version: 2.1.3
% 0.15/0.46 % (3143442)Termination reason: Refutation
% 0.15/0.46 % (3143442)Time elapsed: 0.018 s
% 0.15/0.46 % (3143442)Peak memory usage: 13 MB
% 0.15/0.46 % (3143442)Instructions burned: 52 (million)
% 0.15/0.46 % (3143432)Success in time 0.045 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------