%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP281-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:17:22 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 46
% Syntax : Number of formulae : 313 ( 24 unt; 16 def)
% Number of atoms : 1095 ( 304 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1505 ( 723 ~; 766 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f9]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c2)
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c4) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = inverse(sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c2)
| sk_c8 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = inverse(sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c2)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(sk_c8,X1) != sk_c7
| multiply(X2,sk_c8) != X1
| inverse(X2) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c6) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,X1)
| multiply(X2,sk_c8) != X1
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( multiply(sk_c8,sk_c7) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c6 = multiply(sk_c7,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c6 != multiply(sk_c7,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X2] :
( sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f82,definition,
( spl0_5
<=> ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8 )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,definition,
( spl0_6
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c8,sk_c7) != sk_c6
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f88,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f67,f85,f82,f79,f75,f72,f69]) ).
fof(f90,definition,
( spl0_7
<=> sk_c7 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c8 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c8 = inverse(sk_c2)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f64,f94,f90]) ).
fof(f99,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c5)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_8 ),
inference(avatar_split_clause,[],[f62,f94,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c8 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f105,plain,
( sk_c8 != multiply(sk_c4,sk_c7)
| spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_8 ),
inference(avatar_split_clause,[],[f60,f94,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c4)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f113,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f75]) ).
fof(f115,definition,
( spl0_12
<=> sk_c3 = multiply(sk_c2,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( sk_c3 = multiply(sk_c2,sk_c8)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f118,plain,
( spl0_7
| spl0_12 ),
inference(avatar_split_clause,[],[f54,f115,f90]) ).
fof(f119,plain,
( spl0_9
| spl0_12 ),
inference(avatar_split_clause,[],[f52,f115,f99]) ).
fof(f120,plain,
( spl0_10
| spl0_12 ),
inference(avatar_split_clause,[],[f50,f115,f104]) ).
fof(f121,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f48,f115,f109]) ).
fof(f122,plain,
( spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f46,f115,f75]) ).
fof(f124,definition,
( spl0_13
<=> sk_c7 = multiply(sk_c8,sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f126,plain,
( sk_c7 = multiply(sk_c8,sk_c3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f127,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f124,f90]) ).
fof(f128,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f124,f99]) ).
fof(f129,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f40,f124,f104]) ).
fof(f130,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f38,f124,f109]) ).
fof(f131,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f36,f124,f75]) ).
fof(f133,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f135,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f136,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f133,f90]) ).
fof(f137,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f133,f99]) ).
fof(f138,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f133,f104]) ).
fof(f139,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f28,f133,f109]) ).
fof(f142,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f144,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f145,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f142,f90]) ).
fof(f146,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f142,f99]) ).
fof(f147,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f142,f104]) ).
fof(f148,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f142,f109]) ).
fof(f152,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f85,f104]) ).
fof(f153,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f8,f85,f109]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c7,sk_c5)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c4)
| ~ spl0_11 ),
inference(superposition,[],[f3,f111]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f160,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(sk_c6,X0)
| ~ spl0_3 ),
inference(superposition,[],[f4,f76]) ).
fof(f161,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c7,multiply(sk_c5,X0))
| ~ spl0_9 ),
inference(superposition,[],[f4,f155]) ).
fof(f162,plain,
( ! [X0] : multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f106]) ).
fof(f164,plain,
( ! [X0] : multiply(sk_c7,multiply(sk_c5,X0)) = X0
| ~ spl0_9 ),
inference(forward_demodulation,[],[f161,f1]) ).
fof(f165,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f168,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0))
| ~ spl0_11 ),
inference(superposition,[],[f4,f156]) ).
fof(f169,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c4,X0)) = X0
| ~ spl0_11 ),
inference(forward_demodulation,[],[f168,f1]) ).
fof(f174,plain,
( sk_c6 = multiply(sk_c7,sk_c7)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f164,f92]) ).
fof(f177,plain,
( multiply(sk_c8,sk_c8) = multiply(sk_c4,sk_c6)
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f162,f76]) ).
fof(f191,plain,
( sk_c7 = multiply(sk_c8,sk_c8)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f169,f106]) ).
fof(f200,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f165,f3]) ).
fof(f201,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f165,f165]) ).
fof(f202,plain,
( sk_c4 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f165,f156]) ).
fof(f203,plain,
( ! [X0] : multiply(sk_c4,X0) = multiply(inverse(sk_c8),X0)
| ~ spl0_11 ),
inference(superposition,[],[f165,f169]) ).
fof(f220,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl0_11 ),
inference(forward_demodulation,[],[f202,f203]) ).
fof(f221,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f200,f201]) ).
fof(f229,plain,
( multiply(sk_c7,sk_c7) = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f160,f191]) ).
fof(f233,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f229,f174]) ).
fof(f239,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c6)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f165,f233]) ).
fof(f241,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f239,f3]) ).
fof(f252,plain,
( ! [X0] : multiply(sk_c8,X0) = X0
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f1,f241]) ).
fof(f255,plain,
( sk_c6 = multiply(inverse(sk_c4),multiply(sk_c8,sk_c8))
| ~ spl0_3
| ~ spl0_10 ),
inference(superposition,[],[f165,f177]) ).
fof(f258,plain,
( sk_c6 = multiply(inverse(sk_c4),sk_c7)
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f255,f191]) ).
fof(f260,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| ~ spl0_3
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f258,f111]) ).
fof(f261,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f260,f87]) ).
fof(f262,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f261]) ).
fof(f263,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f80,f252]) ).
fof(f264,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f86,f252]) ).
fof(f266,plain,
( spl0_5
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f263,f109,f104,f99,f90,f79,f75,f82]) ).
fof(f270,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f177,f264]) ).
fof(f274,plain,
( sk_c7 = multiply(sk_c4,sk_c7)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f270,f191]) ).
fof(f276,plain,
( sk_c8 = sk_c7
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f274,f106]) ).
fof(f279,plain,
( identity != sk_c7
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5 ),
inference(superposition,[],[f83,f3]) ).
fof(f280,plain,
( sk_c7 != sk_c7
| sk_c8 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f83,f191]) ).
fof(f283,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f280]) ).
fof(f296,plain,
( identity = multiply(sk_c8,sk_c5)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f155,f276]) ).
fof(f309,plain,
( identity = sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f296,f252]) ).
fof(f314,plain,
( sk_c8 = sk_c5
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f309,f241]) ).
fof(f341,plain,
( sk_c7 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f101,f314]) ).
fof(f350,plain,
( sk_c8 = inverse(sk_c8)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f341,f276]) ).
fof(f355,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f350,f283]) ).
fof(f356,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f359,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f70,f276]) ).
fof(f360,plain,
( ! [X4] :
( sk_c7 != multiply(X4,sk_c7)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f359,f264]) ).
fof(f361,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f360,f276]) ).
fof(f367,plain,
( sk_c8 != sk_c6
| sk_c8 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f361,f233]) ).
fof(f369,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f367,f264]) ).
fof(f374,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f369,f276]) ).
fof(f381,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f374,f264]) ).
fof(f385,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f381,f276]) ).
fof(f388,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f385,f350]) ).
fof(f389,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f390,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f73,f276]) ).
fof(f413,plain,
( sk_c8 != sk_c6
| sk_c8 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f390,f233]) ).
fof(f415,plain,
( sk_c8 != sk_c7
| sk_c8 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f413,f264]) ).
fof(f420,plain,
( sk_c8 != inverse(sk_c6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f415,f276]) ).
fof(f427,plain,
( sk_c8 != inverse(sk_c7)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f420,f264]) ).
fof(f431,plain,
( sk_c8 != inverse(sk_c8)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f427,f276]) ).
fof(f434,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f431,f350]) ).
fof(f435,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f434]) ).
fof(f437,plain,
( identity = multiply(sk_c8,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f96]) ).
fof(f439,plain,
( identity = multiply(sk_c8,sk_c1)
| ~ spl0_14 ),
inference(superposition,[],[f3,f135]) ).
fof(f443,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c3)
| ~ spl0_12 ),
inference(superposition,[],[f165,f117]) ).
fof(f445,plain,
( sk_c8 = multiply(sk_c8,sk_c3)
| ~ spl0_8
| ~ spl0_12 ),
inference(forward_demodulation,[],[f443,f96]) ).
fof(f446,plain,
( sk_c3 = multiply(inverse(sk_c8),sk_c7)
| ~ spl0_13 ),
inference(superposition,[],[f165,f126]) ).
fof(f448,plain,
( multiply(sk_c4,sk_c7) = sk_c3
| ~ spl0_11
| ~ spl0_13 ),
inference(forward_demodulation,[],[f446,f203]) ).
fof(f451,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f165,f144]) ).
fof(f452,plain,
( ! [X0] : multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0))
| ~ spl0_15 ),
inference(superposition,[],[f4,f144]) ).
fof(f453,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f451,f135]) ).
fof(f454,plain,
( sk_c2 = multiply(inverse(sk_c8),identity)
| ~ spl0_8 ),
inference(superposition,[],[f165,f437]) ).
fof(f459,plain,
( sk_c1 = multiply(inverse(sk_c8),identity)
| ~ spl0_14 ),
inference(superposition,[],[f165,f439]) ).
fof(f462,plain,
( sk_c1 = multiply(sk_c4,identity)
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f459,f203]) ).
fof(f463,plain,
( sk_c4 = sk_c1
| ~ spl0_11
| ~ spl0_14 ),
inference(forward_demodulation,[],[f462,f220]) ).
fof(f587,plain,
( multiply(sk_c7,sk_c3) = multiply(sk_c1,sk_c7)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f452,f126]) ).
fof(f594,plain,
( multiply(sk_c4,sk_c7) = multiply(sk_c7,sk_c3)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f587,f463]) ).
fof(f603,plain,
( sk_c3 = multiply(sk_c7,sk_c3)
| ~ spl0_11
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f594,f448]) ).
fof(f611,plain,
( sk_c8 = sk_c7
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f126,f445]) ).
fof(f612,plain,
( multiply(sk_c1,sk_c8) = multiply(sk_c7,sk_c3)
| ~ spl0_8
| ~ spl0_12
| ~ spl0_15 ),
inference(superposition,[],[f452,f445]) ).
fof(f618,plain,
( multiply(sk_c1,sk_c8) = sk_c3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f612,f603]) ).
fof(f619,plain,
( sk_c7 = sk_c3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f618,f144]) ).
fof(f620,plain,
( sk_c8 = sk_c3
| ~ spl0_8
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f619,f611]) ).
fof(f621,plain,
( sk_c8 != sk_c3
| spl0_10
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[],[f105,f448]) ).
fof(f626,plain,
( $false
| ~ spl0_8
| spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f621,f620]) ).
fof(f627,plain,
( ~ spl0_8
| spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f632,plain,
( sk_c2 = inverse(sk_c8)
| ~ spl0_8 ),
inference(forward_demodulation,[],[f454,f221]) ).
fof(f633,plain,
( sk_c1 = inverse(sk_c8)
| ~ spl0_14 ),
inference(forward_demodulation,[],[f459,f221]) ).
fof(f660,plain,
( sk_c6 != multiply(sk_c8,sk_c8)
| spl0_3
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f77,f611]) ).
fof(f661,plain,
( sk_c6 = multiply(sk_c8,sk_c8)
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f86,f611]) ).
fof(f664,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f660,f661]) ).
fof(f665,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f664]) ).
fof(f667,plain,
( ! [X2] :
( sk_c8 != multiply(sk_c8,multiply(X2,sk_c8))
| sk_c8 != inverse(X2) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f80,f611]) ).
fof(f671,plain,
( sk_c8 != multiply(sk_c8,identity)
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f667,f3]) ).
fof(f680,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f671,f221]) ).
fof(f688,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f680,f632]) ).
fof(f704,definition,
( spl0_19
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
fof(f705,plain,
( sk_c8 = sk_c6
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f706,plain,
( sk_c8 != sk_c6
| spl0_19 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f708,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f688,f96]) ).
fof(f709,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f711,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f70,f611]) ).
fof(f713,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c6)
| sk_c8 != inverse(X4) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f711,f611]) ).
fof(f722,plain,
( identity = multiply(sk_c1,sk_c8)
| ~ spl0_14 ),
inference(superposition,[],[f3,f633]) ).
fof(f723,plain,
( identity = sk_c7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f722,f144]) ).
fof(f724,plain,
( identity = sk_c8
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f723,f611]) ).
fof(f727,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f713,f3]) ).
fof(f730,plain,
( sk_c8 != inverse(inverse(sk_c6))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f727,f724]) ).
fof(f829,plain,
( sk_c8 = sk_c6
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f453,f86]) ).
fof(f841,plain,
( $false
| ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(forward_subsumption_resolution,[],[f829,f706]) ).
fof(f842,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f841]) ).
fof(f854,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[],[f730,f705]) ).
fof(f855,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f854,f632]) ).
fof(f858,plain,
( $false
| ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f855,f96]) ).
fof(f859,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f858]) ).
fof(f862,plain,
( ! [X3] :
( sk_c8 != multiply(X3,sk_c8)
| sk_c8 != inverse(X3) )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f73,f611]) ).
fof(f865,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(superposition,[],[f862,f3]) ).
fof(f874,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f865,f724]) ).
fof(f881,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f874,f632]) ).
fof(f883,plain,
( $false
| ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f881,f96]) ).
fof(f884,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f883]) ).
fof(f887,plain,
( identity != sk_c8
| sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f279,f611]) ).
fof(f891,plain,
( sk_c8 != inverse(inverse(sk_c8))
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f887,f724]) ).
fof(f894,plain,
( sk_c8 != inverse(sk_c2)
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f891,f632]) ).
fof(f896,plain,
( $false
| ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f894,f96]) ).
fof(f897,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f896]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| ~ spl0_3
| spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f88]) ).
cnf(s2,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s3,plain,
( spl0_8
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s4,plain,
( spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s5,plain,
( spl0_8
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s6,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
( spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl0_10
| spl0_12 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl0_3
| spl0_12 ),
inference(sat_conversion,[],[f122]) ).
cnf(s12,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f129]) ).
cnf(s15,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f130]) ).
cnf(s16,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f131]) ).
cnf(s17,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f139]) ).
cnf(s22,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s29,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f152]) ).
cnf(s30,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f153]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f262]) ).
cnf(s33,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f266]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f356]) ).
cnf(s39,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f389]) ).
cnf(s44,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f435]) ).
cnf(s47,plain,
( ~ spl0_8
| spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f627]) ).
cnf(s48,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f665]) ).
cnf(s53,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f709]) ).
cnf(s62,plain,
( ~ spl0_6
| ~ spl0_14
| ~ spl0_15
| spl0_19 ),
inference(sat_conversion,[],[f842]) ).
cnf(s64,plain,
( ~ spl0_1
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(sat_conversion,[],[f859]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f884]) ).
cnf(s68,plain,
( ~ spl0_5
| ~ spl0_8
| ~ spl0_12
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f897]) ).
cnf(s69,plain,
spl0_3,
inference(rat,[],[s48,s6,s11,s16,s31]) ).
cnf(s70,plain,
spl0_6,
inference(rat,[],[s32,s29,s30,s69]) ).
cnf(s71,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s68,s10,s15,s20,s25]) ).
cnf(s72,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s68,s9,s14,s19,s24]) ).
cnf(s73,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s68,s8,s13,s18,s23,s34,s72,s71,s69,s70]) ).
cnf(s74,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s34,s3,s4,s5,s73,s70,s69]) ).
cnf(s75,plain,
~ spl0_5,
inference(rat,[],[s68,s2,s7,s12,s17,s22,s74]) ).
cnf(s76,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_4 ),
inference(rat,[],[s53,s10,s15]) ).
cnf(s77,plain,
( spl0_10
| ~ spl0_11
| ~ spl0_8 ),
inference(rat,[],[s47,s9,s14,s19,s24]) ).
cnf(s78,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s53,s8,s13,s33,s77,s76,s69,s75]) ).
cnf(s79,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s33,s3,s4,s5,s78,s75,s69]) ).
cnf(s80,plain,
~ spl0_4,
inference(rat,[],[s53,s2,s7,s12,s79]) ).
cnf(s81,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s67,s10,s15,s20,s25]) ).
cnf(s82,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s67,s8,s13,s18,s23,s44,s77,s81,s69,s70]) ).
cnf(s83,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s44,s3,s4,s5,s82,s70,s69]) ).
cnf(s84,plain,
~ spl0_2,
inference(rat,[],[s67,s2,s7,s12,s17,s22,s83]) ).
cnf(s85,plain,
spl0_1,
inference(rat,[],[s1,s69,s70,s75,s80,s84]) ).
cnf(s86,plain,
( spl0_11
| ~ spl0_8 ),
inference(rat,[],[s64,s62,s10,s15,s20,s25,s85,s70]) ).
cnf(s87,plain,
( ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s64,s62,s8,s13,s18,s23,s39,s77,s86,s85,s70,s69]) ).
cnf(s88,plain,
~ spl0_7,
inference(rat,[],[s39,s3,s4,s5,s87,s69,s70,s85]) ).
cnf(s89,plain,
spl0_15,
inference(rat,[],[s22,s88]) ).
cnf(s90,plain,
spl0_14,
inference(rat,[],[s17,s88]) ).
cnf(s91,plain,
spl0_13,
inference(rat,[],[s12,s88]) ).
cnf(s92,plain,
spl0_12,
inference(rat,[],[s7,s88]) ).
cnf(s93,plain,
spl0_8,
inference(rat,[],[s2,s88]) ).
cnf(s94,plain,
spl0_19,
inference(rat,[],[s62,s89,s70,s90]) ).
cnf(s95,plain,
$false,
inference(rat,[],[s64,s94,s89,s90,s93,s85,s91,s92]) ).
fof(f900,plain,
$false,
inference(avatar_sat_refutation,[],[s95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP281-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 09:47:30 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.16/0.48 % (1412330)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (1412335)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1897439672_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.48 % TRYING [1]
% 0.16/0.48 % TRYING [2]
% 0.16/0.48 % TRYING [3]
% 0.16/0.48 % (1412336)% WARNING: option uhcvi not known.
% 0.16/0.48 % TRYING [4]
% 0.16/0.48 % (1412338)dis+10_1_sil=32000:sp=arity:random_seed=2631078508:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.48 % (1412336)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=809742040:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.48 % (1412337)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2441366231:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.48 % (1412339)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2447414301:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.48 % (1412341)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2707318623:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (1412340)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1028244802:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.48 % TRYING [5]
% 0.16/0.48 % (1412339) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1412330-1412339"...
% 0.16/0.48 % TRYING [6]
% 0.16/0.48 % (1412340) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1412330-1412340"...
% 0.16/0.48 % (1412339)...printing done.
% 0.16/0.48 % (1412341) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1412330-1412341"...
% 0.16/0.48 % (1412338) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1412330-1412338"...
% 0.16/0.48 % (1412339)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (1412339)------------------------------
% 0.16/0.48 % (1412339)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (1412339)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (1412339)CaDiCaL version: 2.1.3
% 0.16/0.48 % (1412339)Termination reason: Refutation
% 0.16/0.48 % (1412339)Time elapsed: 0.019 s
% 0.16/0.48 % (1412339)Peak memory usage: 12 MB
% 0.16/0.48 % (1412339)Instructions burned: 29 (million)
% 0.16/0.48 % (1412330)Success in time 0.056 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------