%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 10:13:37 AM UTC 2026
% Result : Unsatisfiable 2.80s 1.27s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 47
% Syntax : Number of formulae : 314 ( 21 unt; 16 def)
% Number of atoms : 1057 ( 295 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1439 ( 696 ~; 727 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 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 : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f5]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c1,sk_c8) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c1)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c1)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c1) = sk_c8
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c1)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c1) = sk_c8
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c1)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c8,sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = inverse(sk_c2)
| sk_c7 = multiply(sk_c8,sk_c4) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c7 = inverse(sk_c2)
| sk_c4 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c2)
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = inverse(sk_c2)
| sk_c6 = inverse(sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| multiply(X0,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X1,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c8,X2) != sk_c7
| multiply(X3,sk_c8) != X2
| inverse(X3) != sk_c8
| multiply(X4,sk_c6) != sk_c8
| inverse(X4) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(sk_c8,X2)
| multiply(X3,sk_c8) != X2
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4] :
( multiply(sk_c7,sk_c8) != sk_c6
| sk_c7 != multiply(X0,sk_c8)
| inverse(X0) != sk_c8
| sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != multiply(sk_c8,multiply(X3,sk_c8))
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ),
inference(equality_resolution,[],[f66]) ).
fof(f69,definition,
( spl0_1
<=> ! [X4] :
( sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f70,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c6)
| sk_c6 != inverse(X4) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,definition,
( spl0_2
<=> ! [X3] :
( sk_c7 != multiply(sk_c8,multiply(X3,sk_c8))
| sk_c8 != inverse(X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f73,plain,
( ! [X3] :
( sk_c8 != inverse(X3)
| sk_c7 != multiply(sk_c8,multiply(X3,sk_c8)) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f75,definition,
( spl0_3
<=> sk_c7 = multiply(sk_c6,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f76,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f77,plain,
( sk_c7 != multiply(sk_c6,sk_c8)
| spl0_3 ),
inference(avatar_component_clause,[],[f75]) ).
fof(f79,definition,
( spl0_4
<=> ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f80,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c7)
| sk_c7 != inverse(X1) )
| ~ 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_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) != 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_c6 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f92,plain,
( sk_c6 = inverse(sk_c5)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f94,definition,
( spl0_8
<=> sk_c7 = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f96,plain,
( sk_c7 = 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_c8 = multiply(sk_c5,sk_c6) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f101,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| ~ 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 = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f106,plain,
( sk_c8 = inverse(sk_c3)
| ~ 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_c4 = multiply(sk_c3,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f111,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f112,plain,
( spl0_11
| spl0_8 ),
inference(avatar_split_clause,[],[f58,f94,f109]) ).
fof(f114,definition,
( spl0_12
<=> sk_c7 = multiply(sk_c8,sk_c4) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f115,plain,
( sk_c7 != multiply(sk_c8,sk_c4)
| spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f116,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f114]) ).
fof(f117,plain,
( spl0_12
| spl0_8 ),
inference(avatar_split_clause,[],[f56,f94,f114]) ).
fof(f118,plain,
( spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f54,f94,f75]) ).
fof(f120,definition,
( spl0_13
<=> sk_c6 = multiply(sk_c2,sk_c7) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f122,plain,
( sk_c6 = multiply(sk_c2,sk_c7)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f120]) ).
fof(f123,plain,
( spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f52,f120,f90]) ).
fof(f124,plain,
( spl0_9
| spl0_13 ),
inference(avatar_split_clause,[],[f50,f120,f99]) ).
fof(f125,plain,
( spl0_10
| spl0_13 ),
inference(avatar_split_clause,[],[f48,f120,f104]) ).
fof(f126,plain,
( spl0_11
| spl0_13 ),
inference(avatar_split_clause,[],[f46,f120,f109]) ).
fof(f127,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f44,f120,f114]) ).
fof(f128,plain,
( spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f42,f120,f75]) ).
fof(f130,definition,
( spl0_14
<=> sk_c8 = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f132,plain,
( sk_c8 = inverse(sk_c1)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f133,plain,
( spl0_7
| spl0_14 ),
inference(avatar_split_clause,[],[f40,f130,f90]) ).
fof(f134,plain,
( spl0_9
| spl0_14 ),
inference(avatar_split_clause,[],[f38,f130,f99]) ).
fof(f135,plain,
( spl0_10
| spl0_14 ),
inference(avatar_split_clause,[],[f36,f130,f104]) ).
fof(f136,plain,
( spl0_11
| spl0_14 ),
inference(avatar_split_clause,[],[f34,f130,f109]) ).
fof(f137,plain,
( spl0_12
| spl0_14 ),
inference(avatar_split_clause,[],[f32,f130,f114]) ).
fof(f138,plain,
( spl0_3
| spl0_14 ),
inference(avatar_split_clause,[],[f30,f130,f75]) ).
fof(f140,definition,
( spl0_15
<=> sk_c7 = multiply(sk_c1,sk_c8) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f142,plain,
( sk_c7 = multiply(sk_c1,sk_c8)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f143,plain,
( spl0_7
| spl0_15 ),
inference(avatar_split_clause,[],[f28,f140,f90]) ).
fof(f144,plain,
( spl0_9
| spl0_15 ),
inference(avatar_split_clause,[],[f26,f140,f99]) ).
fof(f145,plain,
( spl0_10
| spl0_15 ),
inference(avatar_split_clause,[],[f24,f140,f104]) ).
fof(f146,plain,
( spl0_11
| spl0_15 ),
inference(avatar_split_clause,[],[f22,f140,f109]) ).
fof(f147,plain,
( spl0_12
| spl0_15 ),
inference(avatar_split_clause,[],[f20,f140,f114]) ).
fof(f148,plain,
( spl0_3
| spl0_15 ),
inference(avatar_split_clause,[],[f18,f140,f75]) ).
fof(f149,plain,
( spl0_7
| spl0_6 ),
inference(avatar_split_clause,[],[f16,f85,f90]) ).
fof(f150,plain,
( spl0_9
| spl0_6 ),
inference(avatar_split_clause,[],[f14,f85,f99]) ).
fof(f154,plain,
( spl0_3
| spl0_6 ),
inference(avatar_split_clause,[],[f6,f85,f75]) ).
fof(f155,plain,
( identity = multiply(sk_c6,sk_c5)
| ~ spl0_7 ),
inference(superposition,[],[f3,f92]) ).
fof(f156,plain,
( identity = multiply(sk_c8,sk_c3)
| ~ spl0_10 ),
inference(superposition,[],[f3,f106]) ).
fof(f159,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[],[f4,f3]) ).
fof(f164,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f159,f1]) ).
fof(f167,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c6,multiply(sk_c5,X0))
| ~ spl0_7 ),
inference(superposition,[],[f4,f155]) ).
fof(f168,plain,
( ! [X0] : multiply(sk_c6,multiply(sk_c5,X0)) = X0
| ~ spl0_7 ),
inference(forward_demodulation,[],[f167,f1]) ).
fof(f169,plain,
( ! [X0] : multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0))
| ~ spl0_10 ),
inference(superposition,[],[f4,f156]) ).
fof(f170,plain,
( ! [X0] : multiply(sk_c8,multiply(sk_c3,X0)) = X0
| ~ spl0_10 ),
inference(forward_demodulation,[],[f169,f1]) ).
fof(f171,plain,
( sk_c6 = multiply(sk_c6,sk_c8)
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f168,f101]) ).
fof(f174,plain,
( sk_c7 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f171,f76]) ).
fof(f180,plain,
( sk_c8 = multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f101,f174]) ).
fof(f181,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f76,f174]) ).
fof(f194,plain,
( sk_c7 != sk_c6
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f87,f181]) ).
fof(f196,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f194,f174]) ).
fof(f197,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[],[f196]) ).
fof(f198,plain,
( ! [X1] :
( sk_c7 != inverse(X1)
| sk_c7 != multiply(X1,sk_c7) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f80,f174]) ).
fof(f200,plain,
( sk_c7 != sk_c6
| sk_c7 != multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[],[f198,f92]) ).
fof(f207,definition,
( spl0_17
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f208,plain,
( sk_c7 = sk_c8
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f209,plain,
( sk_c7 != sk_c8
| spl0_17 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f211,plain,
( sk_c7 != multiply(sk_c5,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[],[f200,f174]) ).
fof(f212,plain,
( sk_c7 != sk_c8
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f211,f180]) ).
fof(f213,plain,
( ~ spl0_17
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f212,f99,f90,f79,f75,f207]) ).
fof(f220,plain,
( sk_c8 = multiply(sk_c8,sk_c4)
| ~ spl0_10
| ~ spl0_11 ),
inference(superposition,[],[f170,f111]) ).
fof(f236,plain,
( sk_c7 = sk_c8
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(superposition,[],[f220,f116]) ).
fof(f245,plain,
( $false
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f236,f209]) ).
fof(f246,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f247,plain,
( sk_c7 != sk_c8
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(forward_demodulation,[],[f115,f220]) ).
fof(f248,plain,
( sk_c7 = multiply(sk_c2,sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_demodulation,[],[f122,f174]) ).
fof(f249,plain,
( sk_c7 != sk_c7
| sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(superposition,[],[f198,f96]) ).
fof(f250,plain,
( identity = multiply(sk_c7,sk_c2)
| ~ spl0_8 ),
inference(superposition,[],[f3,f96]) ).
fof(f251,plain,
( sk_c7 != multiply(sk_c2,sk_c7)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f249]) ).
fof(f256,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f251,f248]) ).
fof(f257,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f256]) ).
fof(f261,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_2
| ~ spl0_10 ),
inference(superposition,[],[f73,f106]) ).
fof(f263,plain,
( sk_c8 != sk_c8
| sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_2
| ~ spl0_14 ),
inference(superposition,[],[f73,f132]) ).
fof(f265,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c1,sk_c8))
| ~ spl0_2
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f263]) ).
fof(f266,plain,
( sk_c7 != multiply(sk_c8,multiply(sk_c3,sk_c8))
| ~ spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f261]) ).
fof(f267,plain,
( sk_c7 != multiply(sk_c8,sk_c7)
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f265,f142]) ).
fof(f269,plain,
( sk_c7 != sk_c8
| ~ spl0_2
| ~ spl0_10 ),
inference(forward_demodulation,[],[f266,f170]) ).
fof(f307,plain,
( sk_c2 = multiply(inverse(sk_c7),identity)
| ~ spl0_8 ),
inference(superposition,[],[f164,f250]) ).
fof(f312,plain,
( sk_c8 = multiply(inverse(sk_c6),sk_c7)
| ~ spl0_3 ),
inference(superposition,[],[f164,f76]) ).
fof(f321,plain,
( sk_c8 = multiply(inverse(sk_c1),sk_c7)
| ~ spl0_15 ),
inference(superposition,[],[f164,f142]) ).
fof(f332,plain,
( sk_c8 = multiply(sk_c8,sk_c7)
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f321,f132]) ).
fof(f341,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f312,f174]) ).
fof(f348,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9 ),
inference(forward_demodulation,[],[f341,f3]) ).
fof(f363,plain,
( sk_c7 = multiply(inverse(sk_c2),sk_c6)
| ~ spl0_13 ),
inference(superposition,[],[f164,f122]) ).
fof(f365,plain,
( sk_c7 = multiply(sk_c7,sk_c6)
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f363,f96]) ).
fof(f377,plain,
( sk_c7 != sk_c8
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f267,f332]) ).
fof(f381,plain,
( sk_c7 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f164,f332]) ).
fof(f383,plain,
( identity = sk_c7
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f381,f3]) ).
fof(f425,plain,
( sk_c6 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_13 ),
inference(superposition,[],[f164,f365]) ).
fof(f427,plain,
( identity = sk_c6
| ~ spl0_8
| ~ spl0_13 ),
inference(forward_demodulation,[],[f425,f3]) ).
fof(f429,plain,
( sk_c7 = sk_c6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f427,f383]) ).
fof(f476,plain,
( sk_c8 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f312,f429]) ).
fof(f477,plain,
( identity = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f476,f3]) ).
fof(f480,plain,
( sk_c7 = sk_c8
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(superposition,[],[f383,f477]) ).
fof(f487,plain,
( sk_c7 != multiply(sk_c7,sk_c8)
| spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f77,f429]) ).
fof(f490,plain,
( sk_c7 != sk_c6
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f487,f86]) ).
fof(f493,plain,
( $false
| spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f490,f429]) ).
fof(f494,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f493]) ).
fof(f495,plain,
( sk_c7 = multiply(sk_c7,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f76,f429]) ).
fof(f496,plain,
( spl0_17
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f480,f140,f130,f120,f94,f75,f207]) ).
fof(f500,plain,
( ~ spl0_17
| ~ spl0_10
| ~ spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f247,f114,f109,f104,f207]) ).
fof(f502,plain,
( ~ spl0_17
| ~ spl0_2
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f269,f104,f72,f207]) ).
fof(f503,plain,
( ~ spl0_17
| ~ spl0_2
| ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f377,f140,f130,f72,f207]) ).
fof(f509,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c7)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f70,f429]) ).
fof(f512,plain,
( sk_c2 = multiply(inverse(sk_c7),sk_c7)
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f307,f383]) ).
fof(f514,plain,
( ! [X4] :
( sk_c7 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f509,f429]) ).
fof(f517,plain,
( identity = sk_c2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f512,f3]) ).
fof(f519,plain,
( sk_c7 = sk_c2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15 ),
inference(forward_demodulation,[],[f517,f383]) ).
fof(f544,plain,
( sk_c8 = multiply(sk_c8,sk_c8)
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f495,f208]) ).
fof(f545,plain,
( sk_c8 = sk_c2
| ~ spl0_8
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f519,f208]) ).
fof(f572,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c7) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f514,f208]) ).
fof(f573,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f572,f208]) ).
fof(f579,plain,
( sk_c7 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f573,f96]) ).
fof(f582,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f579,f208]) ).
fof(f586,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_1
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f582,f545]) ).
fof(f589,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f586,f544]) ).
fof(f590,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f589]) ).
fof(f591,plain,
( ! [X1] :
( sk_c6 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f80,f208]) ).
fof(f592,plain,
( ! [X1] :
( sk_c7 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f591,f429]) ).
fof(f593,plain,
( ! [X1] :
( sk_c8 != multiply(X1,sk_c8)
| sk_c7 != inverse(X1) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f592,f208]) ).
fof(f594,plain,
( ! [X1] :
( sk_c8 != inverse(X1)
| sk_c8 != multiply(X1,sk_c8) )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f593,f208]) ).
fof(f598,plain,
( sk_c7 != sk_c8
| sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(superposition,[],[f594,f96]) ).
fof(f601,plain,
( sk_c8 != multiply(sk_c2,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f598,f208]) ).
fof(f605,plain,
( sk_c8 != multiply(sk_c8,sk_c8)
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f601,f545]) ).
fof(f608,plain,
( $false
| ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f605,f544]) ).
fof(f609,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f608]) ).
fof(f610,plain,
( ! [X0] :
( inverse(X0) != sk_c8
| sk_c8 != multiply(X0,sk_c8) )
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_demodulation,[],[f83,f208]) ).
fof(f612,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(superposition,[],[f610,f132]) ).
fof(f614,plain,
( sk_c8 != multiply(sk_c1,sk_c8)
| ~ spl0_5
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f612]) ).
fof(f617,plain,
( sk_c7 != sk_c8
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_demodulation,[],[f614,f142]) ).
fof(f621,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f617,f208]) ).
fof(f622,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f625,plain,
( sk_c8 = sk_c6
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f174,f208]) ).
fof(f636,plain,
( sk_c8 = multiply(sk_c8,sk_c4)
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f116,f208]) ).
fof(f662,plain,
( sk_c4 = multiply(inverse(sk_c8),sk_c8)
| ~ spl0_12
| ~ spl0_17 ),
inference(superposition,[],[f164,f636]) ).
fof(f664,plain,
( identity = sk_c4
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f662,f3]) ).
fof(f668,plain,
( sk_c8 = sk_c4
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f664,f348]) ).
fof(f689,plain,
( ! [X4] :
( sk_c8 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f70,f625]) ).
fof(f690,plain,
( ! [X4] :
( sk_c8 != inverse(X4)
| sk_c8 != multiply(X4,sk_c8) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[],[f689,f625]) ).
fof(f691,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f690,f106]) ).
fof(f694,plain,
( sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f691]) ).
fof(f697,plain,
( sk_c8 != sk_c4
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f694,f111]) ).
fof(f700,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f697,f668]) ).
fof(f701,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f700]) ).
fof(f707,plain,
( sk_c8 != sk_c8
| sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_17 ),
inference(superposition,[],[f610,f106]) ).
fof(f710,plain,
( sk_c8 != multiply(sk_c3,sk_c8)
| ~ spl0_5
| ~ spl0_10
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f707]) ).
fof(f712,plain,
( sk_c8 != sk_c4
| ~ spl0_5
| ~ spl0_10
| ~ spl0_11
| ~ spl0_17 ),
inference(forward_demodulation,[],[f710,f111]) ).
fof(f713,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f712,f668]) ).
fof(f714,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f713]) ).
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_8
| spl0_12 ),
inference(sat_conversion,[],[f117]) ).
cnf(s7,plain,
( spl0_3
| spl0_8 ),
inference(sat_conversion,[],[f118]) ).
cnf(s8,plain,
( spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f123]) ).
cnf(s9,plain,
( spl0_9
| spl0_13 ),
inference(sat_conversion,[],[f124]) ).
cnf(s10,plain,
( spl0_10
| spl0_13 ),
inference(sat_conversion,[],[f125]) ).
cnf(s11,plain,
( spl0_11
| spl0_13 ),
inference(sat_conversion,[],[f126]) ).
cnf(s12,plain,
( spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f127]) ).
cnf(s13,plain,
( spl0_3
| spl0_13 ),
inference(sat_conversion,[],[f128]) ).
cnf(s14,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f133]) ).
cnf(s15,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f134]) ).
cnf(s16,plain,
( spl0_10
| spl0_14 ),
inference(sat_conversion,[],[f135]) ).
cnf(s17,plain,
( spl0_11
| spl0_14 ),
inference(sat_conversion,[],[f136]) ).
cnf(s18,plain,
( spl0_12
| spl0_14 ),
inference(sat_conversion,[],[f137]) ).
cnf(s19,plain,
( spl0_3
| spl0_14 ),
inference(sat_conversion,[],[f138]) ).
cnf(s20,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f143]) ).
cnf(s21,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f144]) ).
cnf(s22,plain,
( spl0_10
| spl0_15 ),
inference(sat_conversion,[],[f145]) ).
cnf(s23,plain,
( spl0_11
| spl0_15 ),
inference(sat_conversion,[],[f146]) ).
cnf(s24,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f147]) ).
cnf(s25,plain,
( spl0_3
| spl0_15 ),
inference(sat_conversion,[],[f148]) ).
cnf(s26,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f149]) ).
cnf(s27,plain,
( spl0_6
| spl0_9 ),
inference(sat_conversion,[],[f150]) ).
cnf(s31,plain,
( spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f154]) ).
cnf(s32,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f197]) ).
cnf(s34,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_9
| ~ spl0_17 ),
inference(sat_conversion,[],[f213]) ).
cnf(s36,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| spl0_17 ),
inference(sat_conversion,[],[f246]) ).
cnf(s37,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| ~ spl0_13 ),
inference(sat_conversion,[],[f257]) ).
cnf(s41,plain,
( spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f494]) ).
cnf(s42,plain,
( ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| spl0_17 ),
inference(sat_conversion,[],[f496]) ).
cnf(s44,plain,
( ~ spl0_10
| ~ spl0_11
| spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f500]) ).
cnf(s45,plain,
( ~ spl0_2
| ~ spl0_10
| ~ spl0_17 ),
inference(sat_conversion,[],[f502]) ).
cnf(s46,plain,
( ~ spl0_2
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f503]) ).
cnf(s49,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f590]) ).
cnf(s52,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_8
| ~ spl0_13
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f609]) ).
cnf(s54,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15
| ~ spl0_17 ),
inference(sat_conversion,[],[f622]) ).
cnf(s57,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f701]) ).
cnf(s59,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9
| ~ spl0_10
| ~ spl0_11
| ~ spl0_12
| ~ spl0_17 ),
inference(sat_conversion,[],[f714]) ).
cnf(s60,plain,
spl0_3,
inference(rat,[],[s41,s7,s13,s19,s25,s31]) ).
cnf(s61,plain,
spl0_6,
inference(rat,[],[s32,s26,s27,s60]) ).
cnf(s62,plain,
( ~ spl0_12
| ~ spl0_11
| ~ spl0_10
| ~ spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(rat,[],[s36,s59,s60]) ).
cnf(s63,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_9
| ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s42,s44,s12,s18,s24,s62,s60]) ).
cnf(s64,plain,
( spl0_11
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s42,s54,s11,s17,s23,s60]) ).
cnf(s65,plain,
( spl0_10
| ~ spl0_8
| ~ spl0_5 ),
inference(rat,[],[s42,s54,s10,s16,s22,s60]) ).
cnf(s66,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_5
| ~ spl0_8
| ~ spl0_7 ),
inference(rat,[],[s42,s54,s9,s15,s21,s63,s60]) ).
cnf(s67,plain,
( ~ spl0_8
| ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s66,s65,s64]) ).
cnf(s68,plain,
( ~ spl0_7
| ~ spl0_5 ),
inference(rat,[],[s62,s3,s4,s5,s6,s67]) ).
cnf(s69,plain,
~ spl0_5,
inference(rat,[],[s42,s54,s2,s8,s14,s20,s68,s60]) ).
cnf(s70,plain,
( ~ spl0_9
| ~ spl0_8
| ~ spl0_11
| ~ spl0_10
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s12,s36,s37,s34,s60]) ).
cnf(s71,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_13
| ~ spl0_4
| ~ spl0_8 ),
inference(rat,[],[s42,s52,s60]) ).
cnf(s72,plain,
( ~ spl0_8
| ~ spl0_11
| ~ spl0_4
| ~ spl0_10
| ~ spl0_7 ),
inference(rat,[],[s71,s9,s15,s21,s70]) ).
cnf(s73,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_4
| ~ spl0_7 ),
inference(rat,[],[s34,s36,s3,s6,s72,s60]) ).
cnf(s74,plain,
( spl0_11
| ~ spl0_4 ),
inference(rat,[],[s71,s5,s11,s17,s23]) ).
cnf(s75,plain,
( spl0_10
| ~ spl0_4 ),
inference(rat,[],[s71,s4,s10,s16,s22]) ).
cnf(s76,plain,
( ~ spl0_10
| ~ spl0_11
| ~ spl0_4 ),
inference(rat,[],[s71,s2,s8,s14,s20,s73]) ).
cnf(s77,plain,
~ spl0_4,
inference(rat,[],[s76,s75,s74]) ).
cnf(s78,plain,
( spl0_12
| spl0_17
| ~ spl0_8 ),
inference(rat,[],[s42,s12,s18,s24,s60]) ).
cnf(s79,plain,
( ~ spl0_10
| ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s42,s11,s17,s23,s36,s78,s45,s60]) ).
cnf(s80,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s42,s46,s10,s16,s22,s79,s60]) ).
cnf(s81,plain,
~ spl0_2,
inference(rat,[],[s45,s36,s4,s5,s6,s80]) ).
cnf(s82,plain,
spl0_1,
inference(rat,[],[s1,s61,s69,s60,s77,s81]) ).
cnf(s83,plain,
( ~ spl0_15
| ~ spl0_14
| ~ spl0_8
| ~ spl0_13 ),
inference(rat,[],[s42,s49,s82,s60]) ).
cnf(s84,plain,
( spl0_15
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s57,s36,s20,s21,s24,s60,s82]) ).
cnf(s85,plain,
( spl0_14
| ~ spl0_11
| ~ spl0_10 ),
inference(rat,[],[s57,s36,s14,s15,s18,s60,s82]) ).
cnf(s86,plain,
( ~ spl0_11
| ~ spl0_10
| ~ spl0_8 ),
inference(rat,[],[s57,s36,s8,s9,s12,s83,s85,s84,s60,s82]) ).
cnf(s87,plain,
( spl0_11
| ~ spl0_8 ),
inference(rat,[],[s83,s11,s17,s23]) ).
cnf(s88,plain,
( ~ spl0_11
| ~ spl0_8 ),
inference(rat,[],[s83,s10,s16,s22,s86]) ).
cnf(s89,plain,
~ spl0_8,
inference(rat,[],[s88,s87]) ).
cnf(s90,plain,
spl0_12,
inference(rat,[],[s6,s89]) ).
cnf(s91,plain,
spl0_11,
inference(rat,[],[s5,s89]) ).
cnf(s92,plain,
spl0_10,
inference(rat,[],[s4,s89]) ).
cnf(s93,plain,
spl0_9,
inference(rat,[],[s3,s89]) ).
cnf(s94,plain,
spl0_7,
inference(rat,[],[s2,s89]) ).
cnf(s95,plain,
spl0_17,
inference(rat,[],[s36,s92,s91,s90]) ).
cnf(s98,plain,
$false,
inference(rat,[],[s57,s95,s90,s91,s82,s60,s92,s94,s93]) ).
fof(f715,plain,
$false,
inference(avatar_sat_refutation,[],[s98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP316-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:53:00 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.80/1.27 % (1416086)Input is clausal, will run a generic CNF schedule.
% 2.80/1.27 % (1416091)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4150334082:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.80/1.27 % (1416096)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=536704490:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.80/1.27 % (1416093)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1856320328:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.80/1.27 % (1416092)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=849924766:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.80/1.27 % (1416094)lrs+10_1_sil=8000:sp=occurrence:random_seed=989375726:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.80/1.27 % (1416097)dis-21_1_sil=8000:lcm=predicate:random_seed=1712518449:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.80/1.27 % (1416095)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4099654437:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.80/1.27 % (1416097)Refutation not found, incomplete strategy
% 2.80/1.27 % (1416097)------------------------------
% 2.80/1.27 % (1416097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.27 % (1416097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.27 % (1416097)CaDiCaL version: 2.1.3
% 2.80/1.27 % (1416097)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.27 % (1416097)Time elapsed: 0.002 s
% 2.80/1.27 % (1416097)Peak memory usage: 88 MB
% 2.80/1.27 % (1416097)Instructions burned: 2 (million)
% 2.80/1.27 % (1416094)Refutation not found, incomplete strategy
% 2.80/1.27 % (1416094)------------------------------
% 2.80/1.27 % (1416094)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.27 % (1416094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.27 % (1416094)CaDiCaL version: 2.1.3
% 2.80/1.27 % (1416094)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.27 % (1416094)Time elapsed: 0.004 s
% 2.80/1.27 % (1416094)Peak memory usage: 88 MB
% 2.80/1.27 % (1416094)Instructions burned: 4 (million)
% 2.80/1.27 % (1416096)First to succeed.
% 2.80/1.27 % (1416096)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1416086"
% 2.80/1.27 % (1416095)Instruction limit reached!
% 2.80/1.27 % (1416095)------------------------------
% 2.80/1.27 % (1416095)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.27 % (1416095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.27 % (1416095)CaDiCaL version: 2.1.3
% 2.80/1.27 % (1416095)Termination reason: Instruction limit
% 2.80/1.27 % (1416095)Termination phase: Saturation
% 2.80/1.27 % (1416095)Time elapsed: 0.066 s
% 2.80/1.27 % (1416095)Peak memory usage: 89 MB
% 2.80/1.27 % (1416095)Instructions burned: 115 (million)
% 2.80/1.27 % (1416105)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3300187066:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 2.80/1.27 % (1416105)Refutation not found, incomplete strategy
% 2.80/1.27 % (1416105)------------------------------
% 2.80/1.27 % (1416105)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.27 % (1416105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.27 % (1416105)CaDiCaL version: 2.1.3
% 2.80/1.27 % (1416105)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.27 % (1416105)Time elapsed: 0.004 s
% 2.80/1.27 % (1416105)Peak memory usage: 88 MB
% 2.80/1.27 % (1416105)Instructions burned: 5 (million)
% 2.80/1.27 % (1416094)------------------------------
% 2.80/1.27 % (1416094)------------------------------
% 2.80/1.27 % (1416097)------------------------------
% 2.80/1.27 % (1416097)------------------------------
% 2.80/1.27 % (1416096)Refutation found. Thanks to Tanya!
% 2.80/1.27 % SZS status Unsatisfiable for theBenchmark
% 2.80/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.47 % (1416096)------------------------------
% 3.61/1.47 % (1416096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.47 % (1416096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.47 % (1416096)CaDiCaL version: 2.1.3
% 3.61/1.47 % (1416096)Termination reason: Refutation
% 3.61/1.47 % (1416096)Time elapsed: 0.021 s
% 3.61/1.47 % (1416096)Peak memory usage: 90 MB
% 3.61/1.47 % (1416096)Instructions burned: 27 (million)
% 3.61/1.47 % (1416096)------------------------------
% 3.61/1.47 % (1416096)------------------------------
% 3.61/1.47 % (1416086)Success in time 0.428 s
% 3.61/1.47 % Vampire exiting
%------------------------------------------------------------------------------