%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP391-1 : 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 : n005.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 10:17:40 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 50
% Syntax : Number of formulae : 328 ( 21 unt; 19 def)
% Number of atoms : 1118 ( 321 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1516 ( 726 ~; 771 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 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,
( inverse(sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( inverse(sk_c6) = sk_c8
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( inverse(sk_c6) = sk_c8
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( inverse(sk_c6) = sk_c8
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( inverse(sk_c6) = sk_c8
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( inverse(sk_c6) = sk_c8
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c1,sk_c2) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c2 = inverse(sk_c1)
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c2 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c1) = sk_c2
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c2 = inverse(sk_c1)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c1) = sk_c2
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c2 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f48]) ).
fof(f52,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c4,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c4) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c5,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c6 = multiply(sk_c5,sk_c8) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c6) != sk_c8
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| multiply(X1,sk_c7) != sk_c8
| multiply(sk_c6,sk_c7) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X3,sk_c7) != sk_c6
| inverse(X3) != sk_c7
| inverse(X4) != sk_c6
| multiply(X4,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( inverse(sk_c6) != sk_c8
| multiply(X0,X1) != sk_c8
| inverse(X0) != X1
| sk_c8 != multiply(X1,sk_c7)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,X4] :
( inverse(sk_c6) != sk_c8
| sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2)
| sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3)
| sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ),
inference(equality_resolution,[],[f65]) ).
fof(f68,definition,
( spl0_1
<=> ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f69,plain,
( ! [X4] :
( sk_c6 != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,definition,
( spl0_2
<=> ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f72,plain,
( ! [X3] :
( sk_c6 != multiply(X3,sk_c7)
| sk_c7 != inverse(X3) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,definition,
( spl0_3
<=> ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f75,plain,
( ! [X2] :
( sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X2) )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f77,definition,
( spl0_4
<=> sk_c8 = multiply(sk_c6,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f78,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( sk_c8 != multiply(sk_c6,sk_c7)
| spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_5
<=> ! [X0] :
( sk_c8 != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f82,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_6
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f85,plain,
( inverse(sk_c6) = sk_c8
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f86,plain,
( inverse(sk_c6) != sk_c8
| spl0_6 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f87,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f66,f84,f81,f77,f74,f71,f68]) ).
fof(f89,definition,
( spl0_7
<=> sk_c6 = multiply(sk_c5,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f90,plain,
( sk_c6 != multiply(sk_c5,sk_c8)
| spl0_7 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl0_7
| spl0_4 ),
inference(avatar_split_clause,[],[f63,f77,f89]) ).
fof(f94,definition,
( spl0_8
<=> sk_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f94]) ).
fof(f97,plain,
( spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f61,f77,f94]) ).
fof(f99,definition,
( spl0_9
<=> sk_c7 = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c7 = inverse(sk_c4)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f99]) ).
fof(f102,plain,
( spl0_9
| spl0_4 ),
inference(avatar_split_clause,[],[f59,f77,f99]) ).
fof(f104,definition,
( spl0_10
<=> sk_c6 = multiply(sk_c4,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f107,plain,
( spl0_10
| spl0_4 ),
inference(avatar_split_clause,[],[f57,f77,f104]) ).
fof(f109,definition,
( spl0_11
<=> sk_c8 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c8 = inverse(sk_c3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_4 ),
inference(avatar_split_clause,[],[f55,f77,f109]) ).
fof(f114,definition,
( spl0_12
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f116,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_4 ),
inference(avatar_split_clause,[],[f53,f77,f114]) ).
fof(f119,definition,
( spl0_13
<=> sk_c8 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f121,plain,
( sk_c8 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f123,plain,
( spl0_8
| spl0_13 ),
inference(avatar_split_clause,[],[f49,f119,f94]) ).
fof(f124,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f47,f119,f99]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f45,f119,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f43,f119,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f41,f119,f114]) ).
fof(f129,definition,
( spl0_14
<=> sk_c2 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f131,plain,
( sk_c2 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f133,plain,
( spl0_8
| spl0_14 ),
inference(avatar_split_clause,[],[f37,f129,f94]) ).
fof(f134,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f35,f129,f99]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f33,f129,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f31,f129,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f29,f129,f114]) ).
fof(f139,definition,
( spl0_15
<=> sk_c8 = multiply(sk_c1,sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f141,plain,
( sk_c8 = multiply(sk_c1,sk_c2)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f143,plain,
( spl0_8
| spl0_15 ),
inference(avatar_split_clause,[],[f25,f139,f94]) ).
fof(f144,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f23,f139,f99]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f21,f139,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f19,f139,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f17,f139,f114]) ).
fof(f148,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f15,f84,f89]) ).
fof(f149,plain,
( spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f13,f84,f94]) ).
fof(f150,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f11,f84,f99]) ).
fof(f151,plain,
( spl0_10
| spl0_6 ),
inference(avatar_split_clause,[],[f9,f84,f104]) ).
fof(f152,plain,
( spl0_11
| spl0_6 ),
inference(avatar_split_clause,[],[f7,f84,f109]) ).
fof(f153,plain,
( spl0_12
| spl0_6 ),
inference(avatar_split_clause,[],[f5,f84,f114]) ).
fof(f154,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_8 ),
inference(superposition,[],[f3,f96]) ).
fof(f155,plain,
( identity = multiply(sk_c7,sk_c4)
| ~ spl0_9 ),
inference(superposition,[],[f3,f101]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ 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(f161,plain,
( ! [X0] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(sk_c6,X0)
| ~ spl0_10 ),
inference(superposition,[],[f4,f106]) ).
fof(f163,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f179,plain,
( multiply(sk_c6,sk_c4) = multiply(sk_c4,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f161,f155]) ).
fof(f201,plain,
( sk_c5 = multiply(inverse(sk_c6),identity)
| ~ spl0_8 ),
inference(superposition,[],[f163,f154]) ).
fof(f204,plain,
( sk_c3 = multiply(inverse(sk_c8),identity)
| ~ spl0_11 ),
inference(superposition,[],[f163,f156]) ).
fof(f205,plain,
( sk_c8 = multiply(inverse(sk_c3),sk_c7)
| ~ spl0_12 ),
inference(superposition,[],[f163,f116]) ).
fof(f207,plain,
( sk_c4 = multiply(inverse(sk_c7),identity)
| ~ spl0_9 ),
inference(superposition,[],[f163,f155]) ).
fof(f209,plain,
( sk_c7 = multiply(inverse(sk_c4),sk_c6)
| ~ spl0_10 ),
inference(superposition,[],[f163,f106]) ).
fof(f218,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f209,f101]) ).
fof(f220,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f205,f111]) ).
fof(f222,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f163,f218]) ).
fof(f224,plain,
( identity = sk_c6
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f222,f3]) ).
fof(f229,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f163,f220]) ).
fof(f231,plain,
( identity = sk_c7
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f229,f3]) ).
fof(f238,plain,
( sk_c8 != multiply(identity,sk_c7)
| spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f79,f224]) ).
fof(f239,plain,
( sk_c8 != sk_c7
| spl0_4
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f238,f1]) ).
fof(f243,plain,
( sk_c5 = multiply(inverse(identity),identity)
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f201,f224]) ).
fof(f244,plain,
( identity = sk_c5
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f243,f3]) ).
fof(f248,plain,
( sk_c6 = multiply(identity,sk_c8)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[],[f91,f244]) ).
fof(f251,plain,
( sk_c6 = sk_c8
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f248,f1]) ).
fof(f255,plain,
( identity = sk_c8
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f251,f224]) ).
fof(f271,plain,
( sk_c4 = multiply(inverse(identity),identity)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f207,f231]) ).
fof(f275,plain,
( identity = sk_c4
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f271,f3]) ).
fof(f303,plain,
( sk_c3 = multiply(inverse(identity),identity)
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f204,f255]) ).
fof(f306,plain,
( identity = sk_c3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f303,f3]) ).
fof(f322,plain,
( identity != sk_c8
| spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f239,f231]) ).
fof(f323,plain,
( $false
| spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f322,f255]) ).
fof(f324,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f323]) ).
fof(f325,plain,
( sk_c8 = multiply(sk_c6,identity)
| ~ spl0_4
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f78,f231]) ).
fof(f326,plain,
( identity != inverse(sk_c6)
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f86,f255]) ).
fof(f327,plain,
( sk_c8 = multiply(identity,identity)
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f325,f224]) ).
fof(f328,plain,
( identity != inverse(identity)
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f326,f224]) ).
fof(f329,plain,
( identity = sk_c8
| ~ spl0_4
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f327,f1]) ).
fof(f330,plain,
( multiply(sk_c4,identity) = multiply(identity,sk_c4)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f179,f224]) ).
fof(f331,plain,
( sk_c4 = multiply(sk_c4,identity)
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f330,f1]) ).
fof(f335,plain,
( sk_c7 = inverse(identity)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f101,f275]) ).
fof(f345,plain,
( identity = inverse(identity)
| ~ spl0_9
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f335,f231]) ).
fof(f349,plain,
( $false
| spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f345,f328]) ).
fof(f350,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f351,plain,
( ! [X0] :
( identity != multiply(X0,inverse(X0))
| sk_c8 != multiply(inverse(X0),sk_c7) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f82,f255]) ).
fof(f352,plain,
( identity = inverse(sk_c6)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f85,f255]) ).
fof(f353,plain,
( ! [X0] :
( sk_c8 != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f351,f231]) ).
fof(f354,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f352,f224]) ).
fof(f355,plain,
( ! [X0] :
( identity != multiply(inverse(X0),identity)
| identity != multiply(X0,inverse(X0)) )
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f353,f255]) ).
fof(f362,plain,
( identity != multiply(sk_c6,identity)
| identity != multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f355,f96]) ).
fof(f371,plain,
( identity != multiply(identity,identity)
| identity != multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f362,f224]) ).
fof(f380,plain,
( identity != multiply(sk_c5,sk_c6)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f371,f1]) ).
fof(f385,plain,
( identity != multiply(sk_c5,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f380,f224]) ).
fof(f390,plain,
( identity != multiply(identity,identity)
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f385,f244]) ).
fof(f395,plain,
( $false
| ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f390,f1]) ).
fof(f396,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f397,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f69,f224]) ).
fof(f398,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f397,f255]) ).
fof(f399,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f398,f224]) ).
fof(f417,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f399,f204]) ).
fof(f426,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f417,f306]) ).
fof(f433,plain,
( identity != inverse(inverse(identity))
| ~ spl0_1
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f426,f255]) ).
fof(f441,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_demodulation,[],[f433,f354]) ).
fof(f444,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[],[f441,f354]) ).
fof(f445,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f446,plain,
( ! [X3] :
( sk_c6 != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f72,f231]) ).
fof(f447,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| sk_c7 != inverse(X3) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f446,f224]) ).
fof(f448,plain,
( ! [X3] :
( identity != multiply(X3,identity)
| identity != inverse(X3) )
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f447,f231]) ).
fof(f455,plain,
( identity != sk_c4
| identity != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f448,f331]) ).
fof(f458,plain,
( identity != inverse(sk_c4)
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f455,f275]) ).
fof(f465,plain,
( identity != sk_c7
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f458,f101]) ).
fof(f471,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f465,f231]) ).
fof(f472,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f471]) ).
fof(f481,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f75,f255]) ).
fof(f482,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f481,f231]) ).
fof(f483,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f482,f255]) ).
fof(f487,plain,
( identity != sk_c3
| identity != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f483,f204]) ).
fof(f496,plain,
( identity != inverse(inverse(sk_c8))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f487,f306]) ).
fof(f503,plain,
( identity != inverse(inverse(identity))
| ~ spl0_3
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f496,f255]) ).
fof(f511,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_demodulation,[],[f503,f354]) ).
fof(f514,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f511,f354]) ).
fof(f515,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f514]) ).
fof(f517,plain,
( sk_c6 != multiply(identity,sk_c8)
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f90,f244]) ).
fof(f521,plain,
( sk_c6 != sk_c8
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f517,f1]) ).
fof(f523,plain,
( identity != sk_c8
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(forward_demodulation,[],[f521,f224]) ).
fof(f541,plain,
( $false
| ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f523,f329]) ).
fof(f542,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f541]) ).
fof(f571,plain,
( identity = multiply(sk_c8,sk_c6)
| ~ spl0_6 ),
inference(superposition,[],[f3,f85]) ).
fof(f577,plain,
( sk_c2 = multiply(inverse(sk_c1),sk_c8)
| ~ spl0_15 ),
inference(superposition,[],[f163,f141]) ).
fof(f579,plain,
( sk_c2 = multiply(sk_c2,sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f577,f131]) ).
fof(f582,plain,
( sk_c8 != multiply(sk_c2,sk_c7)
| sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[],[f82,f131]) ).
fof(f589,definition,
( spl0_17
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f590,plain,
( identity = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f593,plain,
( sk_c8 != multiply(sk_c1,sk_c2)
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f582,f121]) ).
fof(f604,plain,
( $false
| ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f593,f141]) ).
fof(f605,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f604]) ).
fof(f612,plain,
( sk_c6 != sk_c8
| inverse(sk_c6) != sk_c7
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f72,f78]) ).
fof(f621,definition,
( spl0_21
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f623,plain,
( sk_c6 != sk_c8
| spl0_21 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f625,plain,
( sk_c8 != sk_c7
| sk_c6 != sk_c8
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f612,f85]) ).
fof(f631,definition,
( spl0_23
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f632,plain,
( identity = sk_c6
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f645,definition,
( spl0_26
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f646,plain,
( sk_c8 = sk_c7
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f647,plain,
( sk_c8 != sk_c7
| spl0_26 ),
inference(avatar_component_clause,[],[f645]) ).
fof(f648,plain,
( ~ spl0_21
| ~ spl0_26
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f625,f84,f77,f71,f645,f621]) ).
fof(f661,plain,
( sk_c8 = multiply(inverse(sk_c2),sk_c2)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f163,f579]) ).
fof(f663,plain,
( identity = sk_c8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f661,f3]) ).
fof(f664,plain,
( spl0_17
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f663,f139,f129,f589]) ).
fof(f668,plain,
( identity = multiply(identity,sk_c6)
| ~ spl0_6
| ~ spl0_17 ),
inference(superposition,[],[f571,f590]) ).
fof(f671,plain,
( identity != sk_c6
| ~ spl0_17
| spl0_21 ),
inference(superposition,[],[f623,f590]) ).
fof(f673,plain,
( identity = sk_c6
| ~ spl0_6
| ~ spl0_17 ),
inference(forward_demodulation,[],[f668,f1]) ).
fof(f677,plain,
( ~ spl0_23
| ~ spl0_17
| spl0_21 ),
inference(avatar_split_clause,[],[f671,f621,f589,f631]) ).
fof(f678,plain,
( spl0_23
| ~ spl0_6
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f673,f589,f84,f631]) ).
fof(f680,plain,
( identity != sk_c7
| ~ spl0_17
| spl0_26 ),
inference(forward_demodulation,[],[f647,f590]) ).
fof(f682,plain,
( sk_c8 = multiply(identity,sk_c7)
| ~ spl0_4
| ~ spl0_23 ),
inference(superposition,[],[f78,f632]) ).
fof(f683,plain,
( sk_c8 = inverse(identity)
| ~ spl0_6
| ~ spl0_23 ),
inference(superposition,[],[f85,f632]) ).
fof(f692,plain,
( identity = inverse(identity)
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f683,f590]) ).
fof(f693,plain,
( sk_c8 = sk_c7
| ~ spl0_4
| ~ spl0_23 ),
inference(forward_demodulation,[],[f682,f1]) ).
fof(f695,plain,
( identity = sk_c7
| ~ spl0_4
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f693,f590]) ).
fof(f710,plain,
( $false
| ~ spl0_4
| ~ spl0_17
| ~ spl0_23
| spl0_26 ),
inference(forward_subsumption_resolution,[],[f695,f680]) ).
fof(f711,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_23
| spl0_26 ),
inference(avatar_contradiction_clause,[],[f710]) ).
fof(f712,plain,
( ! [X4] :
( identity != inverse(X4)
| sk_c6 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_23 ),
inference(forward_demodulation,[],[f69,f632]) ).
fof(f713,plain,
( identity = sk_c7
| ~ spl0_17
| ~ spl0_26 ),
inference(forward_demodulation,[],[f646,f590]) ).
fof(f714,plain,
( ! [X4] :
( sk_c6 != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f712,f590]) ).
fof(f715,plain,
( ! [X4] :
( identity != multiply(X4,identity)
| identity != inverse(X4) )
| ~ spl0_1
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_demodulation,[],[f714,f632]) ).
fof(f716,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_23 ),
inference(superposition,[],[f715,f1]) ).
fof(f720,plain,
( identity != inverse(identity)
| ~ spl0_1
| ~ spl0_17
| ~ spl0_23 ),
inference(trivial_inequality_removal,[],[f716]) ).
fof(f740,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f692,f720]) ).
fof(f741,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f740]) ).
fof(f742,plain,
( ! [X2] :
( sk_c7 != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f75,f590]) ).
fof(f743,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| sk_c8 != inverse(X2) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_26 ),
inference(forward_demodulation,[],[f742,f713]) ).
fof(f744,plain,
( ! [X2] :
( identity != multiply(X2,identity)
| identity != inverse(X2) )
| ~ spl0_3
| ~ spl0_17
| ~ spl0_26 ),
inference(forward_demodulation,[],[f743,f590]) ).
fof(f745,plain,
( identity != identity
| identity != inverse(identity)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_26 ),
inference(superposition,[],[f744,f1]) ).
fof(f749,plain,
( identity != inverse(identity)
| ~ spl0_3
| ~ spl0_17
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f745]) ).
fof(f751,plain,
( $false
| ~ spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f692,f749]) ).
fof(f752,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f751]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3
| ~ spl0_4
| spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f87]) ).
cnf(s2,plain,
( spl0_4
| spl0_7 ),
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
( spl0_4
| spl0_8 ),
inference(sat_conversion,[],[f97]) ).
cnf(s4,plain,
( spl0_4
| spl0_9 ),
inference(sat_conversion,[],[f102]) ).
cnf(s5,plain,
( spl0_4
| spl0_10 ),
inference(sat_conversion,[],[f107]) ).
cnf(s6,plain,
( spl0_4
| spl0_11 ),
inference(sat_conversion,[],[f112]) ).
cnf(s7,plain,
( spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s9,plain,
( spl0_8
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s10,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s11,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s13,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s15,plain,
( spl0_8
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s16,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s17,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s18,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s19,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s21,plain,
( spl0_8
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s22,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s23,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s24,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s25,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f148]) ).
cnf(s27,plain,
( spl0_6
| spl0_8 ),
inference(sat_conversion,[],[f149]) ).
cnf(s28,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s29,plain,
( spl0_6
| spl0_10 ),
inference(sat_conversion,[],[f151]) ).
cnf(s30,plain,
( spl0_6
| spl0_11 ),
inference(sat_conversion,[],[f152]) ).
cnf(s31,plain,
( spl0_6
| spl0_12 ),
inference(sat_conversion,[],[f153]) ).
cnf(s32,plain,
( spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f324]) ).
cnf(s33,plain,
( spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f350]) ).
cnf(s39,plain,
( ~ spl0_5
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f396]) ).
cnf(s45,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11 ),
inference(sat_conversion,[],[f445]) ).
cnf(s48,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f472]) ).
cnf(s57,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f515]) ).
cnf(s58,plain,
( ~ spl0_4
| spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f542]) ).
cnf(s63,plain,
( ~ spl0_5
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f605]) ).
cnf(s67,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6
| ~ spl0_21
| ~ spl0_26 ),
inference(sat_conversion,[],[f648]) ).
cnf(s68,plain,
( ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f664]) ).
cnf(s70,plain,
( ~ spl0_17
| spl0_21
| ~ spl0_23 ),
inference(sat_conversion,[],[f677]) ).
cnf(s71,plain,
( ~ spl0_6
| ~ spl0_17
| spl0_23 ),
inference(sat_conversion,[],[f678]) ).
cnf(s74,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_23
| spl0_26 ),
inference(sat_conversion,[],[f711]) ).
cnf(s76,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23 ),
inference(sat_conversion,[],[f741]) ).
cnf(s77,plain,
( ~ spl0_3
| ~ spl0_6
| ~ spl0_17
| ~ spl0_23
| ~ spl0_26 ),
inference(sat_conversion,[],[f752]) ).
cnf(s78,plain,
spl0_4,
inference(rat,[],[s32,s2,s3,s4,s5,s6,s7]) ).
cnf(s79,plain,
spl0_6,
inference(rat,[],[s33,s26,s27,s28,s29,s30,s31]) ).
cnf(s80,plain,
( spl0_12
| ~ spl0_5 ),
inference(rat,[],[s63,s13,s19,s25]) ).
cnf(s81,plain,
( spl0_11
| ~ spl0_5 ),
inference(rat,[],[s63,s12,s18,s24]) ).
cnf(s82,plain,
( spl0_10
| ~ spl0_5 ),
inference(rat,[],[s63,s11,s17,s23]) ).
cnf(s83,plain,
( spl0_9
| ~ spl0_5 ),
inference(rat,[],[s63,s10,s16,s22]) ).
cnf(s84,plain,
( spl0_8
| ~ spl0_5 ),
inference(rat,[],[s63,s9,s15,s21]) ).
cnf(s85,plain,
~ spl0_5,
inference(rat,[],[s39,s58,s84,s83,s82,s81,s80,s78]) ).
cnf(s86,plain,
( ~ spl0_23
| ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s74,s77,s79,s78]) ).
cnf(s87,plain,
( ~ spl0_17
| ~ spl0_3 ),
inference(rat,[],[s86,s71,s79]) ).
cnf(s88,plain,
( spl0_12
| spl0_17 ),
inference(rat,[],[s68,s19,s25]) ).
cnf(s89,plain,
( spl0_11
| spl0_17 ),
inference(rat,[],[s68,s18,s24]) ).
cnf(s90,plain,
( spl0_10
| spl0_17 ),
inference(rat,[],[s68,s17,s23]) ).
cnf(s91,plain,
( spl0_9
| spl0_17 ),
inference(rat,[],[s68,s16,s22]) ).
cnf(s92,plain,
( spl0_8
| spl0_17 ),
inference(rat,[],[s68,s15,s21]) ).
cnf(s93,plain,
~ spl0_3,
inference(rat,[],[s57,s58,s92,s91,s90,s89,s88,s87,s79,s78]) ).
cnf(s94,plain,
( ~ spl0_17
| ~ spl0_2 ),
inference(rat,[],[s67,s74,s70,s71,s79,s78]) ).
cnf(s95,plain,
~ spl0_2,
inference(rat,[],[s48,s91,s90,s89,s88,s94]) ).
cnf(s96,plain,
spl0_1,
inference(rat,[],[s1,s79,s78,s85,s93,s95]) ).
cnf(s97,plain,
~ spl0_17,
inference(rat,[],[s76,s71,s79,s96]) ).
cnf(s98,plain,
spl0_12,
inference(rat,[],[s88,s97]) ).
cnf(s99,plain,
spl0_11,
inference(rat,[],[s89,s97]) ).
cnf(s100,plain,
spl0_10,
inference(rat,[],[s90,s97]) ).
cnf(s101,plain,
spl0_9,
inference(rat,[],[s91,s97]) ).
cnf(s102,plain,
spl0_8,
inference(rat,[],[s92,s97]) ).
cnf(s103,plain,
~ spl0_7,
inference(rat,[],[s45,s101,s102,s96,s79,s99,s100]) ).
cnf(s104,plain,
$false,
inference(rat,[],[s58,s98,s99,s100,s101,s78,s102,s103]) ).
fof(f753,plain,
$false,
inference(avatar_sat_refutation,[],[s104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP391-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.35 % Computer : n005.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 10:00:47 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (3753302)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3753307)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3750742794_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % TRYING [1]
% 0.11/0.45 % TRYING [2]
% 0.11/0.45 % TRYING [3]
% 0.11/0.45 % (3753308)% WARNING: option uhcvi not known.
% 0.11/0.45 % TRYING [4]
% 0.11/0.45 % (3753313)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3254903497:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (3753309)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2798944944:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (3753310)dis+10_1_sil=32000:sp=arity:random_seed=2832899193:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (3753311)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=61508273:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (3753312)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=763604274:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (3753308)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3494407208:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % TRYING [5]
% 0.11/0.45 % (3753310) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3753302-3753310"...
% 0.11/0.45 % TRYING [6]
% 0.11/0.45 % (3753310)...printing done.
% 0.11/0.45 % (3753310)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3753310)------------------------------
% 0.11/0.45 % (3753310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3753310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3753310)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3753310)Termination reason: Refutation
% 0.11/0.45 % (3753310)Time elapsed: 0.016 s
% 0.11/0.45 % (3753310)Peak memory usage: 12 MB
% 0.11/0.45 % (3753310)Instructions burned: 24 (million)
% 0.11/0.45 % (3753302)Success in time 0.052 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------