%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP180-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 10:13:13 AM UTC 2026
% Result : Unsatisfiable 70.08s 12.45s
% Output : Refutation 82.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 50
% Syntax : Number of formulae : 313 ( 115 unt; 33 def)
% Number of atoms : 603 ( 230 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 559 ( 269 ~; 262 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 169 ( 0 sgn 169 !; 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,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_gld) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_3) ).
fof(f21,negated_conjecture,
multiply(a,multiply(inverse(greatest_lower_bound(a,b)),b)) != least_upper_bound(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p11) ).
fof(f22,definition,
sF0 = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f23,plain,
greatest_lower_bound(a,b) = sF0,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF1 = inverse(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f25,plain,
inverse(sF0) = sF1,
inference(reorient_equations,[],[f24]) ).
fof(f26,definition,
sF2 = multiply(sF1,b),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f27,plain,
multiply(sF1,b) = sF2,
inference(reorient_equations,[],[f26]) ).
fof(f28,definition,
sF3 = multiply(a,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f29,plain,
multiply(a,sF2) = sF3,
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
sF4 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f31,plain,
least_upper_bound(a,b) = sF4,
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
sF3 != sF4,
inference(definition_folding,[],[f21,f31,f29,f27,f25,f23]) ).
fof(f34,definition,
( spl5_1
<=> greatest_lower_bound(a,b) = sF0 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f36,plain,
( greatest_lower_bound(a,b) = sF0
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
spl5_1,
inference(avatar_split_clause,[],[f23,f34]) ).
fof(f38,plain,
( a = least_upper_bound(a,sF0)
| ~ spl5_1 ),
inference(superposition,[],[f11,f36]) ).
fof(f39,plain,
( a = least_upper_bound(sF0,a)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f38,f6]) ).
fof(f41,definition,
( spl5_2
<=> least_upper_bound(a,b) = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f43,plain,
( least_upper_bound(a,b) = sF4
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,plain,
spl5_2,
inference(avatar_split_clause,[],[f31,f41]) ).
fof(f46,plain,
( a = greatest_lower_bound(a,sF4)
| ~ spl5_2 ),
inference(superposition,[],[f12,f43]) ).
fof(f48,plain,
( a = greatest_lower_bound(sF4,a)
| ~ spl5_2 ),
inference(forward_demodulation,[],[f46,f5]) ).
fof(f50,definition,
( spl5_3
<=> multiply(a,sF2) = sF3 ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f52,plain,
( multiply(a,sF2) = sF3
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
spl5_3,
inference(avatar_split_clause,[],[f29,f50]) ).
fof(f55,definition,
( spl5_4
<=> sF3 = sF4 ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
fof(f57,plain,
( sF3 != sF4
| spl5_4 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
~ spl5_4,
inference(avatar_split_clause,[],[f32,f55]) ).
fof(f60,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f62,definition,
( spl5_5
<=> multiply(sF1,b) = sF2 ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
fof(f64,plain,
( multiply(sF1,b) = sF2
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f65,plain,
spl5_5,
inference(avatar_split_clause,[],[f27,f62]) ).
fof(f67,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f69,definition,
( spl5_6
<=> inverse(sF0) = sF1 ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
fof(f71,plain,
( inverse(sF0) = sF1
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f69]) ).
fof(f72,plain,
spl5_6,
inference(avatar_split_clause,[],[f25,f69]) ).
fof(f73,plain,
( sF0 = inverse(sF1)
| ~ spl5_6 ),
inference(superposition,[],[f19,f71]) ).
fof(f74,plain,
( ! [X0] : multiply(a,least_upper_bound(sF2,X0)) = least_upper_bound(sF3,multiply(a,X0))
| ~ spl5_3 ),
inference(superposition,[],[f13,f52]) ).
fof(f99,plain,
( ! [X0] : multiply(sF1,greatest_lower_bound(X0,b)) = greatest_lower_bound(multiply(sF1,X0),sF2)
| ~ spl5_5 ),
inference(superposition,[],[f14,f64]) ).
fof(f110,plain,
( ! [X0] : greatest_lower_bound(sF2,multiply(sF1,X0)) = multiply(sF1,greatest_lower_bound(X0,b))
| ~ spl5_5 ),
inference(forward_demodulation,[],[f99,f5]) ).
fof(f116,plain,
( ! [X0] : multiply(a,multiply(sF2,X0)) = multiply(sF3,X0)
| ~ spl5_3 ),
inference(superposition,[],[f4,f52]) ).
fof(f161,plain,
( b = least_upper_bound(b,sF0)
| ~ spl5_1 ),
inference(superposition,[],[f60,f36]) ).
fof(f162,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(least_upper_bound(X0,X1),X0),
inference(superposition,[],[f60,f12]) ).
fof(f168,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X0,least_upper_bound(X0,X1)),
inference(forward_demodulation,[],[f162,f6]) ).
fof(f169,plain,
( b = least_upper_bound(sF0,b)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f161,f6]) ).
fof(f201,plain,
( b = greatest_lower_bound(b,sF4)
| ~ spl5_2 ),
inference(superposition,[],[f67,f43]) ).
fof(f209,plain,
( b = greatest_lower_bound(sF4,b)
| ~ spl5_2 ),
inference(forward_demodulation,[],[f201,f5]) ).
fof(f244,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(superposition,[],[f3,f19]) ).
fof(f245,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f246,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f13,f3]) ).
fof(f248,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[],[f14,f3]) ).
fof(f249,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[],[f14,f3]) ).
fof(f251,plain,
! [X0,X1] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f15,f3]) ).
fof(f253,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(superposition,[],[f16,f3]) ).
fof(f256,plain,
! [X0,X1] : greatest_lower_bound(identity,multiply(inverse(X0),X1)) = multiply(inverse(X0),greatest_lower_bound(X1,X0)),
inference(forward_demodulation,[],[f249,f5]) ).
fof(f258,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f245,f1]) ).
fof(f262,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[],[f258,f19]) ).
fof(f264,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[],[f258,f4]) ).
fof(f265,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f258,f3]) ).
fof(f269,plain,
( b = multiply(inverse(sF1),sF2)
| ~ spl5_5 ),
inference(superposition,[],[f258,f64]) ).
fof(f272,plain,
! [X2,X0,X1] : multiply(inverse(X1),least_upper_bound(X2,multiply(X1,X0))) = least_upper_bound(multiply(inverse(X1),X2),X0),
inference(superposition,[],[f13,f258]) ).
fof(f284,plain,
( b = multiply(sF0,sF2)
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_demodulation,[],[f269,f73]) ).
fof(f285,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f265,f19]) ).
fof(f294,plain,
! [X0,X1] : greatest_lower_bound(identity,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(inverse(X0),X1)),
inference(superposition,[],[f14,f244]) ).
fof(f298,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,X1),inverse(X1)) = greatest_lower_bound(multiply(X0,inverse(X1)),identity),
inference(superposition,[],[f16,f244]) ).
fof(f305,plain,
! [X0,X1] : multiply(greatest_lower_bound(X0,X1),inverse(X1)) = greatest_lower_bound(identity,multiply(X0,inverse(X1))),
inference(forward_demodulation,[],[f298,f5]) ).
fof(f325,plain,
! [X0,X1] : multiply(inverse(greatest_lower_bound(inverse(X1),X0)),greatest_lower_bound(identity,multiply(X0,X1))) = X1,
inference(superposition,[],[f258,f253]) ).
fof(f361,plain,
! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X1),X0)),least_upper_bound(identity,multiply(X0,X1))) = X1,
inference(superposition,[],[f258,f251]) ).
fof(f390,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[],[f20,f19]) ).
fof(f392,plain,
( ! [X0] : inverse(multiply(sF0,X0)) = multiply(inverse(X0),sF1)
| ~ spl5_6 ),
inference(superposition,[],[f20,f71]) ).
fof(f393,plain,
! [X0,X1] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[],[f20,f19]) ).
fof(f399,plain,
! [X2,X0,X1] : multiply(inverse(X1),multiply(inverse(X0),X2)) = multiply(inverse(multiply(X0,X1)),X2),
inference(superposition,[],[f4,f20]) ).
fof(f406,plain,
! [X2,X0,X1] : multiply(greatest_lower_bound(X2,inverse(X1)),inverse(X0)) = greatest_lower_bound(multiply(X2,inverse(X0)),inverse(multiply(X0,X1))),
inference(superposition,[],[f16,f20]) ).
fof(f409,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(inverse(X1)),inverse(multiply(X0,X1))),
inference(superposition,[],[f258,f20]) ).
fof(f410,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(multiply(X0,X1),inverse(X1))),
inference(forward_demodulation,[],[f409,f20]) ).
fof(f417,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f410,f390]) ).
fof(f420,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))),
inference(superposition,[],[f417,f417]) ).
fof(f434,plain,
! [X2,X0,X1] : multiply(inverse(X0),X2) = multiply(X1,multiply(inverse(multiply(X0,X1)),X2)),
inference(superposition,[],[f4,f417]) ).
fof(f459,plain,
! [X0,X1] : inverse(X1) = inverse(multiply(inverse(X0),multiply(X0,X1))),
inference(forward_demodulation,[],[f420,f20]) ).
fof(f466,plain,
! [X0,X1] : inverse(X1) = multiply(inverse(multiply(X0,X1)),X0),
inference(forward_demodulation,[],[f459,f393]) ).
fof(f556,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,X1),greatest_lower_bound(multiply(X0,X2),X3)) = greatest_lower_bound(multiply(X0,greatest_lower_bound(X1,X2)),X3),
inference(superposition,[],[f7,f14]) ).
fof(f579,plain,
( ! [X0] : multiply(inverse(X0),sF0) = inverse(multiply(sF1,X0))
| ~ spl5_6 ),
inference(superposition,[],[f393,f71]) ).
fof(f619,plain,
( ! [X0] : multiply(sF0,inverse(X0)) = inverse(multiply(X0,sF1))
| ~ spl5_6 ),
inference(superposition,[],[f390,f71]) ).
fof(f682,definition,
( spl5_8
<=> b = multiply(sF0,sF2) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f684,plain,
( b = multiply(sF0,sF2)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f682]) ).
fof(f685,plain,
( spl5_8
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f284,f69,f62,f682]) ).
fof(f696,plain,
( inverse(sF0) = multiply(sF2,inverse(b))
| ~ spl5_8 ),
inference(superposition,[],[f417,f684]) ).
fof(f697,plain,
( sF1 = multiply(sF2,inverse(b))
| ~ spl5_6
| ~ spl5_8 ),
inference(forward_demodulation,[],[f696,f71]) ).
fof(f1496,plain,
( greatest_lower_bound(identity,multiply(inverse(b),a)) = multiply(inverse(b),sF0)
| ~ spl5_1 ),
inference(superposition,[],[f256,f36]) ).
fof(f1533,plain,
( inverse(multiply(sF1,b)) = greatest_lower_bound(identity,multiply(inverse(b),a))
| ~ spl5_1
| ~ spl5_6 ),
inference(forward_demodulation,[],[f1496,f579]) ).
fof(f1551,plain,
( inverse(sF2) = greatest_lower_bound(identity,multiply(inverse(b),a))
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(forward_demodulation,[],[f1533,f64]) ).
fof(f1827,definition,
( spl5_9
<=> sF1 = multiply(sF2,inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
fof(f1829,plain,
( sF1 = multiply(sF2,inverse(b))
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f1827]) ).
fof(f1830,plain,
( spl5_9
| ~ spl5_6
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f697,f682,f69,f1827]) ).
fof(f2136,definition,
( spl5_10
<=> a = least_upper_bound(sF0,a) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
fof(f2138,plain,
( a = least_upper_bound(sF0,a)
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f2136]) ).
fof(f2139,plain,
( spl5_10
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f39,f34,f2136]) ).
fof(f2154,plain,
( ! [X0] : multiply(sF0,multiply(sF1,X0)) = X0
| ~ spl5_6 ),
inference(superposition,[],[f262,f71]) ).
fof(f2171,plain,
! [X2,X0,X1] : multiply(X1,greatest_lower_bound(X2,multiply(inverse(X1),X0))) = greatest_lower_bound(multiply(X1,X2),X0),
inference(superposition,[],[f14,f262]) ).
fof(f2281,definition,
( spl5_11
<=> inverse(sF2) = greatest_lower_bound(identity,multiply(inverse(b),a)) ),
introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition]) ).
fof(f2283,plain,
( inverse(sF2) = greatest_lower_bound(identity,multiply(inverse(b),a))
| ~ spl5_11 ),
inference(avatar_component_clause,[],[f2281]) ).
fof(f2284,plain,
( spl5_11
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_split_clause,[],[f1551,f69,f62,f34,f2281]) ).
fof(f2374,plain,
! [X2,X3,X0,X1] : greatest_lower_bound(multiply(X0,greatest_lower_bound(X3,X2)),multiply(X1,X2)) = greatest_lower_bound(multiply(X0,X3),multiply(greatest_lower_bound(X0,X1),X2)),
inference(superposition,[],[f556,f16]) ).
fof(f2608,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(a,greatest_lower_bound(X0,X1)),multiply(b,X1)) = greatest_lower_bound(multiply(a,X0),multiply(sF0,X1))
| ~ spl5_1 ),
inference(superposition,[],[f2374,f36]) ).
fof(f2648,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(a,X0),multiply(sF0,X1)) = greatest_lower_bound(multiply(b,X1),multiply(a,greatest_lower_bound(X0,X1)))
| ~ spl5_1 ),
inference(forward_demodulation,[],[f2608,f5]) ).
fof(f3257,plain,
( multiply(sF3,inverse(b)) = multiply(a,sF1)
| ~ spl5_3
| ~ spl5_9 ),
inference(superposition,[],[f116,f1829]) ).
fof(f3341,definition,
( spl5_14
<=> a = greatest_lower_bound(sF4,a) ),
introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition]) ).
fof(f3343,plain,
( a = greatest_lower_bound(sF4,a)
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f3341]) ).
fof(f3344,plain,
( spl5_14
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f48,f41,f3341]) ).
fof(f3349,plain,
( multiply(inverse(a),a) = greatest_lower_bound(identity,multiply(inverse(a),sF4))
| ~ spl5_14 ),
inference(superposition,[],[f256,f3343]) ).
fof(f3355,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(a),sF4))
| ~ spl5_14 ),
inference(forward_demodulation,[],[f3349,f3]) ).
fof(f4096,definition,
( spl5_18
<=> b = least_upper_bound(sF0,b) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
fof(f4098,plain,
( b = least_upper_bound(sF0,b)
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f4096]) ).
fof(f4099,plain,
( spl5_18
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f169,f34,f4096]) ).
fof(f4103,plain,
( multiply(inverse(sF0),b) = least_upper_bound(identity,multiply(inverse(sF0),b))
| ~ spl5_18 ),
inference(superposition,[],[f246,f4098]) ).
fof(f4111,plain,
( multiply(sF1,b) = least_upper_bound(identity,multiply(sF1,b))
| ~ spl5_6
| ~ spl5_18 ),
inference(forward_demodulation,[],[f4103,f71]) ).
fof(f4113,plain,
( sF2 = least_upper_bound(identity,sF2)
| ~ spl5_5
| ~ spl5_6
| ~ spl5_18 ),
inference(forward_demodulation,[],[f4111,f64]) ).
fof(f4115,plain,
( sF2 = least_upper_bound(sF2,identity)
| ~ spl5_5
| ~ spl5_6
| ~ spl5_18 ),
inference(forward_demodulation,[],[f4113,f6]) ).
fof(f4118,definition,
( spl5_19
<=> sF2 = least_upper_bound(sF2,identity) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
fof(f4120,plain,
( sF2 = least_upper_bound(sF2,identity)
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f4118]) ).
fof(f4121,plain,
( spl5_19
| ~ spl5_5
| ~ spl5_6
| ~ spl5_18 ),
inference(avatar_split_clause,[],[f4115,f4096,f69,f62,f4118]) ).
fof(f4122,plain,
( multiply(a,sF2) = least_upper_bound(sF3,multiply(a,identity))
| ~ spl5_3
| ~ spl5_19 ),
inference(superposition,[],[f74,f4120]) ).
fof(f4138,plain,
( multiply(a,sF2) = least_upper_bound(sF3,a)
| ~ spl5_3
| ~ spl5_19 ),
inference(forward_demodulation,[],[f4122,f285]) ).
fof(f4144,plain,
( sF3 = least_upper_bound(sF3,a)
| ~ spl5_3
| ~ spl5_19 ),
inference(forward_demodulation,[],[f4138,f52]) ).
fof(f4150,definition,
( spl5_20
<=> sF3 = least_upper_bound(sF3,a) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
fof(f4152,plain,
( sF3 = least_upper_bound(sF3,a)
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f4150]) ).
fof(f4153,plain,
( spl5_20
| ~ spl5_3
| ~ spl5_19 ),
inference(avatar_split_clause,[],[f4144,f4118,f50,f4150]) ).
fof(f4154,plain,
( ! [X0] : least_upper_bound(sF3,least_upper_bound(a,X0)) = least_upper_bound(sF3,X0)
| ~ spl5_20 ),
inference(superposition,[],[f8,f4152]) ).
fof(f4488,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(identity,multiply(inverse(X0),X1))),multiply(inverse(X0),multiply(greatest_lower_bound(X1,X0),X2))) = X2,
inference(superposition,[],[f264,f256]) ).
fof(f4709,plain,
! [X2,X0,X1] : multiply(inverse(multiply(X0,greatest_lower_bound(identity,multiply(inverse(X0),X1)))),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f4488,f399]) ).
fof(f4770,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(multiply(X0,identity),X1)),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f4709,f2171]) ).
fof(f4798,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(X0,X1)),multiply(greatest_lower_bound(X1,X0),X2)) = X2,
inference(forward_demodulation,[],[f4770,f285]) ).
fof(f4867,plain,
! [X2,X0,X1] : multiply(inverse(greatest_lower_bound(X2,X1)),X0) = multiply(inverse(greatest_lower_bound(X1,X2)),X0),
inference(superposition,[],[f4798,f262]) ).
fof(f5172,plain,
! [X0,X1] : multiply(inverse(least_upper_bound(inverse(X0),X1)),least_upper_bound(identity,multiply(least_upper_bound(inverse(X0),X1),X0))) = X0,
inference(superposition,[],[f361,f168]) ).
fof(f5187,plain,
! [X0,X1] : least_upper_bound(multiply(inverse(least_upper_bound(inverse(X0),X1)),identity),X0) = X0,
inference(forward_demodulation,[],[f5172,f272]) ).
fof(f5204,plain,
! [X0,X1] : least_upper_bound(X0,multiply(inverse(least_upper_bound(inverse(X0),X1)),identity)) = X0,
inference(forward_demodulation,[],[f5187,f6]) ).
fof(f5207,plain,
! [X0,X1] : least_upper_bound(X0,inverse(least_upper_bound(inverse(X0),X1))) = X0,
inference(forward_demodulation,[],[f5204,f285]) ).
fof(f5215,plain,
! [X0,X1] : inverse(X0) = least_upper_bound(inverse(X0),inverse(least_upper_bound(X0,X1))),
inference(superposition,[],[f5207,f19]) ).
fof(f5319,plain,
( inverse(sF0) = least_upper_bound(inverse(sF0),inverse(a))
| ~ spl5_10 ),
inference(superposition,[],[f5215,f2138]) ).
fof(f5347,plain,
( sF1 = least_upper_bound(sF1,inverse(a))
| ~ spl5_6
| ~ spl5_10 ),
inference(forward_demodulation,[],[f5319,f71]) ).
fof(f5366,definition,
( spl5_24
<=> sF1 = least_upper_bound(sF1,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_24])],[avatar_definition]) ).
fof(f5368,plain,
( sF1 = least_upper_bound(sF1,inverse(a))
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f5366]) ).
fof(f5369,plain,
( spl5_24
| ~ spl5_6
| ~ spl5_10 ),
inference(avatar_split_clause,[],[f5347,f2136,f69,f5366]) ).
fof(f5373,plain,
( inverse(a) = greatest_lower_bound(inverse(a),sF1)
| ~ spl5_24 ),
inference(superposition,[],[f67,f5368]) ).
fof(f5384,plain,
( inverse(a) = greatest_lower_bound(sF1,inverse(a))
| ~ spl5_24 ),
inference(forward_demodulation,[],[f5373,f5]) ).
fof(f5390,definition,
( spl5_25
<=> inverse(a) = greatest_lower_bound(sF1,inverse(a)) ),
introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition]) ).
fof(f5392,plain,
( inverse(a) = greatest_lower_bound(sF1,inverse(a))
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f5390]) ).
fof(f5393,plain,
( spl5_25
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f5384,f5366,f5390]) ).
fof(f5800,definition,
( spl5_27
<=> multiply(sF3,inverse(b)) = multiply(a,sF1) ),
introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition]) ).
fof(f5802,plain,
( multiply(sF3,inverse(b)) = multiply(a,sF1)
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f5800]) ).
fof(f5803,plain,
( spl5_27
| ~ spl5_3
| ~ spl5_9 ),
inference(avatar_split_clause,[],[f3257,f1827,f50,f5800]) ).
fof(f5819,plain,
( inverse(b) = multiply(inverse(greatest_lower_bound(inverse(inverse(b)),sF3)),greatest_lower_bound(identity,multiply(a,sF1)))
| ~ spl5_27 ),
inference(superposition,[],[f325,f5802]) ).
fof(f5838,plain,
( inverse(b) = multiply(inverse(greatest_lower_bound(sF3,inverse(inverse(b)))),greatest_lower_bound(identity,multiply(a,sF1)))
| ~ spl5_27 ),
inference(forward_demodulation,[],[f5819,f4867]) ).
fof(f5844,plain,
( inverse(b) = multiply(inverse(greatest_lower_bound(sF3,b)),greatest_lower_bound(identity,multiply(a,sF1)))
| ~ spl5_27 ),
inference(forward_demodulation,[],[f5838,f19]) ).
fof(f7840,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(a)),sF1)) = multiply(inverse(inverse(a)),inverse(a))
| ~ spl5_25 ),
inference(superposition,[],[f256,f5392]) ).
fof(f7856,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(a)),sF1)) = inverse(multiply(a,inverse(a)))
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7840,f20]) ).
fof(f7863,plain,
( greatest_lower_bound(identity,multiply(inverse(inverse(a)),sF1)) = multiply(a,inverse(a))
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7856,f390]) ).
fof(f7868,plain,
( identity = greatest_lower_bound(identity,multiply(inverse(inverse(a)),sF1))
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7863,f244]) ).
fof(f7873,plain,
( identity = greatest_lower_bound(identity,inverse(multiply(sF0,inverse(a))))
| ~ spl5_6
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7868,f392]) ).
fof(f7874,plain,
( identity = greatest_lower_bound(identity,multiply(a,inverse(sF0)))
| ~ spl5_6
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7873,f390]) ).
fof(f7875,plain,
( identity = greatest_lower_bound(identity,multiply(a,sF1))
| ~ spl5_6
| ~ spl5_25 ),
inference(forward_demodulation,[],[f7874,f71]) ).
fof(f7878,plain,
( inverse(b) = multiply(inverse(greatest_lower_bound(sF3,b)),identity)
| ~ spl5_6
| ~ spl5_25
| ~ spl5_27 ),
inference(backward_demodulation,[],[f5844,f7875]) ).
fof(f7879,plain,
( inverse(b) = inverse(greatest_lower_bound(sF3,b))
| ~ spl5_6
| ~ spl5_25
| ~ spl5_27 ),
inference(forward_demodulation,[],[f7878,f285]) ).
fof(f8178,definition,
( spl5_33
<=> inverse(b) = inverse(greatest_lower_bound(sF3,b)) ),
introduced(definition,[new_symbols(definition,[spl5_33])],[avatar_definition]) ).
fof(f8180,plain,
( inverse(b) = inverse(greatest_lower_bound(sF3,b))
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f8178]) ).
fof(f8181,plain,
( spl5_33
| ~ spl5_6
| ~ spl5_25
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f7879,f5800,f5390,f69,f8178]) ).
fof(f8186,plain,
( inverse(inverse(b)) = greatest_lower_bound(sF3,b)
| ~ spl5_33 ),
inference(superposition,[],[f19,f8180]) ).
fof(f8233,plain,
( b = greatest_lower_bound(sF3,b)
| ~ spl5_33 ),
inference(forward_demodulation,[],[f8186,f19]) ).
fof(f8262,definition,
( spl5_34
<=> b = greatest_lower_bound(sF3,b) ),
introduced(definition,[new_symbols(definition,[spl5_34])],[avatar_definition]) ).
fof(f8264,plain,
( b = greatest_lower_bound(sF3,b)
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f8262]) ).
fof(f8265,plain,
( spl5_34
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f8233,f8178,f8262]) ).
fof(f8268,plain,
( sF3 = least_upper_bound(sF3,b)
| ~ spl5_34 ),
inference(superposition,[],[f11,f8264]) ).
fof(f8295,definition,
( spl5_35
<=> sF3 = least_upper_bound(sF3,b) ),
introduced(definition,[new_symbols(definition,[spl5_35])],[avatar_definition]) ).
fof(f8297,plain,
( sF3 = least_upper_bound(sF3,b)
| ~ spl5_35 ),
inference(avatar_component_clause,[],[f8295]) ).
fof(f8298,plain,
( spl5_35
| ~ spl5_34 ),
inference(avatar_split_clause,[],[f8268,f8262,f8295]) ).
fof(f8372,definition,
( spl5_36
<=> b = greatest_lower_bound(sF4,b) ),
introduced(definition,[new_symbols(definition,[spl5_36])],[avatar_definition]) ).
fof(f8374,plain,
( b = greatest_lower_bound(sF4,b)
| ~ spl5_36 ),
inference(avatar_component_clause,[],[f8372]) ).
fof(f8375,plain,
( spl5_36
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f209,f41,f8372]) ).
fof(f8376,plain,
( multiply(sF1,b) = greatest_lower_bound(sF2,multiply(sF1,sF4))
| ~ spl5_5
| ~ spl5_36 ),
inference(superposition,[],[f110,f8374]) ).
fof(f8397,plain,
( sF2 = greatest_lower_bound(sF2,multiply(sF1,sF4))
| ~ spl5_5
| ~ spl5_36 ),
inference(forward_demodulation,[],[f8376,f64]) ).
fof(f13592,plain,
( least_upper_bound(sF3,b) = least_upper_bound(sF3,sF4)
| ~ spl5_2
| ~ spl5_20 ),
inference(superposition,[],[f4154,f43]) ).
fof(f13652,plain,
( sF3 = least_upper_bound(sF3,sF4)
| ~ spl5_2
| ~ spl5_20
| ~ spl5_35 ),
inference(forward_demodulation,[],[f13592,f8297]) ).
fof(f18613,plain,
! [X2,X0,X1] : multiply(greatest_lower_bound(X1,inverse(inverse(multiply(X0,X2)))),inverse(X2)) = greatest_lower_bound(multiply(X1,inverse(X2)),inverse(inverse(X0))),
inference(superposition,[],[f406,f417]) ).
fof(f18801,plain,
! [X2,X0,X1] : greatest_lower_bound(multiply(X1,inverse(X2)),X0) = multiply(greatest_lower_bound(X1,inverse(inverse(multiply(X0,X2)))),inverse(X2)),
inference(forward_demodulation,[],[f18613,f19]) ).
fof(f18870,plain,
! [X2,X0,X1] : greatest_lower_bound(multiply(X1,inverse(X2)),X0) = multiply(greatest_lower_bound(X1,multiply(X0,X2)),inverse(X2)),
inference(forward_demodulation,[],[f18801,f19]) ).
fof(f18953,definition,
( spl5_57
<=> sF3 = least_upper_bound(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_57])],[avatar_definition]) ).
fof(f18955,plain,
( sF3 = least_upper_bound(sF3,sF4)
| ~ spl5_57 ),
inference(avatar_component_clause,[],[f18953]) ).
fof(f18956,plain,
( spl5_57
| ~ spl5_2
| ~ spl5_20
| ~ spl5_35 ),
inference(avatar_split_clause,[],[f13652,f8295,f4150,f41,f18953]) ).
fof(f18959,plain,
( sF4 = greatest_lower_bound(sF4,sF3)
| ~ spl5_57 ),
inference(superposition,[],[f67,f18955]) ).
fof(f18992,plain,
( sF4 = greatest_lower_bound(sF3,sF4)
| ~ spl5_57 ),
inference(forward_demodulation,[],[f18959,f5]) ).
fof(f18999,definition,
( spl5_58
<=> sF4 = greatest_lower_bound(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl5_58])],[avatar_definition]) ).
fof(f19001,plain,
( sF4 = greatest_lower_bound(sF3,sF4)
| ~ spl5_58 ),
inference(avatar_component_clause,[],[f18999]) ).
fof(f19002,plain,
( spl5_58
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f18992,f18953,f18999]) ).
fof(f23006,plain,
( multiply(inverse(sF2),inverse(a)) = greatest_lower_bound(multiply(identity,inverse(a)),inverse(b))
| ~ spl5_11 ),
inference(superposition,[],[f18870,f2283]) ).
fof(f23134,plain,
( multiply(inverse(sF2),inverse(a)) = greatest_lower_bound(inverse(b),multiply(identity,inverse(a)))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f23006,f5]) ).
fof(f23247,plain,
( multiply(inverse(sF2),inverse(a)) = greatest_lower_bound(inverse(b),inverse(a))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f23134,f1]) ).
fof(f23300,plain,
( greatest_lower_bound(inverse(a),inverse(b)) = multiply(inverse(sF2),inverse(a))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f23247,f5]) ).
fof(f23326,plain,
( inverse(multiply(a,sF2)) = greatest_lower_bound(inverse(a),inverse(b))
| ~ spl5_11 ),
inference(forward_demodulation,[],[f23300,f20]) ).
fof(f23334,plain,
( inverse(sF3) = greatest_lower_bound(inverse(a),inverse(b))
| ~ spl5_3
| ~ spl5_11 ),
inference(forward_demodulation,[],[f23326,f52]) ).
fof(f23341,definition,
( spl5_61
<=> inverse(sF3) = greatest_lower_bound(inverse(a),inverse(b)) ),
introduced(definition,[new_symbols(definition,[spl5_61])],[avatar_definition]) ).
fof(f23343,plain,
( inverse(sF3) = greatest_lower_bound(inverse(a),inverse(b))
| ~ spl5_61 ),
inference(avatar_component_clause,[],[f23341]) ).
fof(f23344,plain,
( spl5_61
| ~ spl5_3
| ~ spl5_11 ),
inference(avatar_split_clause,[],[f23334,f2281,f50,f23341]) ).
fof(f23346,plain,
( multiply(a,inverse(sF3)) = greatest_lower_bound(identity,multiply(a,inverse(b)))
| ~ spl5_61 ),
inference(superposition,[],[f294,f23343]) ).
fof(f40020,plain,
( multiply(sF0,inverse(b)) = greatest_lower_bound(identity,multiply(a,inverse(b)))
| ~ spl5_1 ),
inference(superposition,[],[f305,f36]) ).
fof(f40357,plain,
( multiply(sF0,inverse(b)) = multiply(a,inverse(sF3))
| ~ spl5_1
| ~ spl5_61 ),
inference(forward_demodulation,[],[f40020,f23346]) ).
fof(f40489,plain,
( inverse(multiply(b,sF1)) = multiply(a,inverse(sF3))
| ~ spl5_1
| ~ spl5_6
| ~ spl5_61 ),
inference(forward_demodulation,[],[f40357,f619]) ).
fof(f40743,definition,
( spl5_73
<=> inverse(multiply(b,sF1)) = multiply(a,inverse(sF3)) ),
introduced(definition,[new_symbols(definition,[spl5_73])],[avatar_definition]) ).
fof(f40745,plain,
( inverse(multiply(b,sF1)) = multiply(a,inverse(sF3))
| ~ spl5_73 ),
inference(avatar_component_clause,[],[f40743]) ).
fof(f40746,plain,
( spl5_73
| ~ spl5_1
| ~ spl5_6
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f40489,f23341,f69,f34,f40743]) ).
fof(f40780,plain,
( ! [X0] : multiply(inverse(a),X0) = multiply(inverse(sF3),multiply(inverse(inverse(multiply(b,sF1))),X0))
| ~ spl5_73 ),
inference(superposition,[],[f434,f40745]) ).
fof(f40819,plain,
( ! [X0] : multiply(inverse(a),X0) = multiply(inverse(multiply(inverse(multiply(b,sF1)),sF3)),X0)
| ~ spl5_73 ),
inference(forward_demodulation,[],[f40780,f399]) ).
fof(f40849,plain,
( ! [X0] : multiply(inverse(a),X0) = multiply(multiply(inverse(sF3),multiply(b,sF1)),X0)
| ~ spl5_73 ),
inference(forward_demodulation,[],[f40819,f393]) ).
fof(f40872,plain,
( ! [X0] : multiply(inverse(a),X0) = multiply(inverse(sF3),multiply(multiply(b,sF1),X0))
| ~ spl5_73 ),
inference(forward_demodulation,[],[f40849,f4]) ).
fof(f40881,plain,
( ! [X0] : multiply(inverse(a),X0) = multiply(inverse(sF3),multiply(b,multiply(sF1,X0)))
| ~ spl5_73 ),
inference(forward_demodulation,[],[f40872,f4]) ).
fof(f73167,definition,
( spl5_94
<=> sF2 = greatest_lower_bound(sF2,multiply(sF1,sF4)) ),
introduced(definition,[new_symbols(definition,[spl5_94])],[avatar_definition]) ).
fof(f73169,plain,
( sF2 = greatest_lower_bound(sF2,multiply(sF1,sF4))
| ~ spl5_94 ),
inference(avatar_component_clause,[],[f73167]) ).
fof(f73170,plain,
( spl5_94
| ~ spl5_5
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f8397,f8372,f62,f73167]) ).
fof(f73203,plain,
( greatest_lower_bound(multiply(a,sF2),multiply(sF0,multiply(sF1,sF4))) = greatest_lower_bound(multiply(b,multiply(sF1,sF4)),multiply(a,sF2))
| ~ spl5_1
| ~ spl5_94 ),
inference(superposition,[],[f2648,f73169]) ).
fof(f73227,plain,
( greatest_lower_bound(multiply(a,sF2),multiply(sF0,multiply(sF1,sF4))) = greatest_lower_bound(multiply(a,sF2),multiply(b,multiply(sF1,sF4)))
| ~ spl5_1
| ~ spl5_94 ),
inference(forward_demodulation,[],[f73203,f5]) ).
fof(f73256,plain,
( greatest_lower_bound(sF3,multiply(sF0,multiply(sF1,sF4))) = greatest_lower_bound(sF3,multiply(b,multiply(sF1,sF4)))
| ~ spl5_1
| ~ spl5_3
| ~ spl5_94 ),
inference(forward_demodulation,[],[f73227,f52]) ).
fof(f73272,plain,
( greatest_lower_bound(sF3,sF4) = greatest_lower_bound(sF3,multiply(b,multiply(sF1,sF4)))
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6
| ~ spl5_94 ),
inference(forward_demodulation,[],[f73256,f2154]) ).
fof(f73281,plain,
( sF4 = greatest_lower_bound(sF3,multiply(b,multiply(sF1,sF4)))
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6
| ~ spl5_58
| ~ spl5_94 ),
inference(forward_demodulation,[],[f73272,f19001]) ).
fof(f73687,definition,
( spl5_95
<=> sF4 = greatest_lower_bound(sF3,multiply(b,multiply(sF1,sF4))) ),
introduced(definition,[new_symbols(definition,[spl5_95])],[avatar_definition]) ).
fof(f73689,plain,
( sF4 = greatest_lower_bound(sF3,multiply(b,multiply(sF1,sF4)))
| ~ spl5_95 ),
inference(avatar_component_clause,[],[f73687]) ).
fof(f73690,plain,
( spl5_95
| ~ spl5_1
| ~ spl5_3
| ~ spl5_6
| ~ spl5_58
| ~ spl5_94 ),
inference(avatar_split_clause,[],[f73281,f73167,f18999,f69,f50,f34,f73687]) ).
fof(f73697,plain,
( multiply(inverse(sF3),sF4) = greatest_lower_bound(identity,multiply(inverse(sF3),multiply(b,multiply(sF1,sF4))))
| ~ spl5_95 ),
inference(superposition,[],[f248,f73689]) ).
fof(f73759,plain,
( greatest_lower_bound(identity,multiply(inverse(a),sF4)) = multiply(inverse(sF3),sF4)
| ~ spl5_73
| ~ spl5_95 ),
inference(forward_demodulation,[],[f73697,f40881]) ).
fof(f73780,plain,
( identity = multiply(inverse(sF3),sF4)
| ~ spl5_14
| ~ spl5_73
| ~ spl5_95 ),
inference(forward_demodulation,[],[f73759,f3355]) ).
fof(f73807,definition,
( spl5_97
<=> identity = multiply(inverse(sF3),sF4) ),
introduced(definition,[new_symbols(definition,[spl5_97])],[avatar_definition]) ).
fof(f73809,plain,
( identity = multiply(inverse(sF3),sF4)
| ~ spl5_97 ),
inference(avatar_component_clause,[],[f73807]) ).
fof(f73810,plain,
( spl5_97
| ~ spl5_14
| ~ spl5_73
| ~ spl5_95 ),
inference(avatar_split_clause,[],[f73780,f73687,f40743,f3341,f73807]) ).
fof(f73839,plain,
( sF4 = multiply(inverse(greatest_lower_bound(inverse(sF4),inverse(sF3))),greatest_lower_bound(identity,identity))
| ~ spl5_97 ),
inference(superposition,[],[f325,f73809]) ).
fof(f73851,plain,
( inverse(sF4) = multiply(inverse(identity),inverse(sF3))
| ~ spl5_97 ),
inference(superposition,[],[f466,f73809]) ).
fof(f73926,plain,
( inverse(sF4) = inverse(multiply(sF3,identity))
| ~ spl5_97 ),
inference(forward_demodulation,[],[f73851,f20]) ).
fof(f73938,plain,
( sF4 = multiply(inverse(greatest_lower_bound(inverse(sF3),inverse(sF4))),greatest_lower_bound(identity,identity))
| ~ spl5_97 ),
inference(forward_demodulation,[],[f73839,f4867]) ).
fof(f73990,plain,
( inverse(sF3) = inverse(sF4)
| ~ spl5_97 ),
inference(forward_demodulation,[],[f73926,f285]) ).
fof(f74002,plain,
( sF4 = multiply(inverse(greatest_lower_bound(inverse(sF3),inverse(sF4))),identity)
| ~ spl5_97 ),
inference(forward_demodulation,[],[f73938,f10]) ).
fof(f74176,plain,
( sF4 = inverse(greatest_lower_bound(inverse(sF3),inverse(sF4)))
| ~ spl5_97 ),
inference(forward_demodulation,[],[f74002,f285]) ).
fof(f74717,plain,
( sF4 = inverse(greatest_lower_bound(inverse(sF3),inverse(sF3)))
| ~ spl5_97 ),
inference(forward_demodulation,[],[f74176,f73990]) ).
fof(f74924,plain,
( sF4 = inverse(inverse(sF3))
| ~ spl5_97 ),
inference(forward_demodulation,[],[f74717,f10]) ).
fof(f75029,plain,
( sF3 = sF4
| ~ spl5_97 ),
inference(forward_demodulation,[],[f74924,f19]) ).
fof(f75047,plain,
( $false
| spl5_4
| ~ spl5_97 ),
inference(forward_subsumption_resolution,[],[f75029,f57]) ).
fof(f75048,plain,
( spl5_4
| ~ spl5_97 ),
inference(avatar_contradiction_clause,[],[f75047]) ).
cnf(s1,plain,
spl5_1,
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
spl5_2,
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
spl5_3,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
~ spl5_4,
inference(sat_conversion,[],[f58]) ).
cnf(s5,plain,
spl5_5,
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
spl5_6,
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( ~ spl5_5
| ~ spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f685]) ).
cnf(s9,plain,
( ~ spl5_6
| ~ spl5_8
| spl5_9 ),
inference(sat_conversion,[],[f1830]) ).
cnf(s10,plain,
( ~ spl5_1
| spl5_10 ),
inference(sat_conversion,[],[f2139]) ).
cnf(s11,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6
| spl5_11 ),
inference(sat_conversion,[],[f2284]) ).
cnf(s14,plain,
( ~ spl5_2
| spl5_14 ),
inference(sat_conversion,[],[f3344]) ).
cnf(s18,plain,
( ~ spl5_1
| spl5_18 ),
inference(sat_conversion,[],[f4099]) ).
cnf(s19,plain,
( ~ spl5_5
| ~ spl5_6
| ~ spl5_18
| spl5_19 ),
inference(sat_conversion,[],[f4121]) ).
cnf(s20,plain,
( ~ spl5_3
| ~ spl5_19
| spl5_20 ),
inference(sat_conversion,[],[f4153]) ).
cnf(s24,plain,
( ~ spl5_6
| ~ spl5_10
| spl5_24 ),
inference(sat_conversion,[],[f5369]) ).
cnf(s25,plain,
( ~ spl5_24
| spl5_25 ),
inference(sat_conversion,[],[f5393]) ).
cnf(s27,plain,
( ~ spl5_3
| ~ spl5_9
| spl5_27 ),
inference(sat_conversion,[],[f5803]) ).
cnf(s33,plain,
( ~ spl5_6
| ~ spl5_25
| ~ spl5_27
| spl5_33 ),
inference(sat_conversion,[],[f8181]) ).
cnf(s34,plain,
( ~ spl5_33
| spl5_34 ),
inference(sat_conversion,[],[f8265]) ).
cnf(s35,plain,
( ~ spl5_34
| spl5_35 ),
inference(sat_conversion,[],[f8298]) ).
cnf(s36,plain,
( ~ spl5_2
| spl5_36 ),
inference(sat_conversion,[],[f8375]) ).
cnf(s57,plain,
( ~ spl5_2
| ~ spl5_20
| ~ spl5_35
| spl5_57 ),
inference(sat_conversion,[],[f18956]) ).
cnf(s58,plain,
( ~ spl5_57
| spl5_58 ),
inference(sat_conversion,[],[f19002]) ).
cnf(s61,plain,
( ~ spl5_3
| ~ spl5_11
| spl5_61 ),
inference(sat_conversion,[],[f23344]) ).
cnf(s73,plain,
( ~ spl5_1
| ~ spl5_6
| ~ spl5_61
| spl5_73 ),
inference(sat_conversion,[],[f40746]) ).
cnf(s94,plain,
( ~ spl5_5
| ~ spl5_36
| spl5_94 ),
inference(sat_conversion,[],[f73170]) ).
cnf(s95,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_6
| ~ spl5_58
| ~ spl5_94
| spl5_95 ),
inference(sat_conversion,[],[f73690]) ).
cnf(s97,plain,
( ~ spl5_14
| ~ spl5_73
| ~ spl5_95
| spl5_97 ),
inference(sat_conversion,[],[f73810]) ).
cnf(s121,plain,
( spl5_4
| ~ spl5_97 ),
inference(sat_conversion,[],[f75048]) ).
cnf(s129,plain,
spl5_8,
inference(rat,[],[s8,s6,s5]) ).
cnf(s130,plain,
spl5_9,
inference(rat,[],[s9,s6,s129]) ).
cnf(s131,plain,
~ spl5_97,
inference(rat,[],[s121,s4]) ).
cnf(s135,plain,
spl5_27,
inference(rat,[],[s27,s130,s3]) ).
cnf(s142,plain,
spl5_36,
inference(rat,[],[s36,s2]) ).
cnf(s143,plain,
spl5_14,
inference(rat,[],[s14,s2]) ).
cnf(s144,plain,
spl5_94,
inference(rat,[],[s94,s5,s142]) ).
cnf(s152,plain,
spl5_18,
inference(rat,[],[s18,s1]) ).
cnf(s153,plain,
spl5_11,
inference(rat,[],[s11,s5,s6,s1]) ).
cnf(s154,plain,
spl5_10,
inference(rat,[],[s10,s1]) ).
cnf(s157,plain,
spl5_19,
inference(rat,[],[s19,s5,s6,s152]) ).
cnf(s159,plain,
spl5_61,
inference(rat,[],[s61,s3,s153]) ).
cnf(s163,plain,
spl5_24,
inference(rat,[],[s24,s6,s154]) ).
cnf(s170,plain,
spl5_20,
inference(rat,[],[s20,s3,s157]) ).
cnf(s172,plain,
spl5_73,
inference(rat,[],[s73,s1,s6,s159]) ).
cnf(s178,plain,
spl5_25,
inference(rat,[],[s25,s163]) ).
cnf(s188,plain,
~ spl5_95,
inference(rat,[],[s97,s131,s143,s172]) ).
cnf(s193,plain,
spl5_33,
inference(rat,[],[s33,s135,s6,s178]) ).
cnf(s199,plain,
~ spl5_58,
inference(rat,[],[s95,s1,s144,s3,s6,s188]) ).
cnf(s201,plain,
spl5_34,
inference(rat,[],[s34,s193]) ).
cnf(s204,plain,
~ spl5_57,
inference(rat,[],[s58,s199]) ).
cnf(s208,plain,
spl5_35,
inference(rat,[],[s35,s201]) ).
cnf(s209,plain,
$false,
inference(rat,[],[s57,s170,s2,s204,s208]) ).
fof(f75093,plain,
$false,
inference(avatar_sat_refutation,[],[s209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP180-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n015.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 09:39:15 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 70.08/12.45 % (1406297)Detected a unit-equality problem, will run specialized UEQ schedule.
% 70.08/12.45 % (1406344)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=706739203:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 70.08/12.45 % (1406345)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2478219990:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 70.08/12.45 % (1406341)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=814463536:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 70.08/12.45 % (1406342)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2831924347:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 70.08/12.45 % (1406343)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4163141757:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 70.08/12.45 % (1406344)Instruction limit reached!
% 70.08/12.45 % (1406344)------------------------------
% 70.08/12.45 % (1406344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406344)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406344)Termination reason: Instruction limit
% 70.08/12.45 % (1406344)Termination phase: Saturation
% 70.08/12.45 % (1406344)Time elapsed: 0.069 s
% 70.08/12.45 % (1406344)Peak memory usage: 89 MB
% 70.08/12.45 % (1406344)Instructions burned: 137 (million)
% 70.08/12.45 % (1406346)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2513621302:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 70.08/12.45 % (1406347)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3908544299:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 70.08/12.45 % (1406345)Instruction limit reached!
% 70.08/12.45 % (1406345)------------------------------
% 70.08/12.45 % (1406345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406345)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406345)Termination reason: Instruction limit
% 70.08/12.45 % (1406345)Termination phase: Saturation
% 70.08/12.45 % (1406345)Time elapsed: 0.176 s
% 70.08/12.45 % (1406345)Peak memory usage: 89 MB
% 70.08/12.45 % (1406345)Instructions burned: 181 (million)
% 70.08/12.45 % (1406355)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3134976493:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 70.08/12.45 % (1406346)Instruction limit reached!
% 70.08/12.45 % (1406346)------------------------------
% 70.08/12.45 % (1406346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406346)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406346)Termination reason: Instruction limit
% 70.08/12.45 % (1406346)Termination phase: Saturation
% 70.08/12.45 % (1406346)Time elapsed: 0.260 s
% 70.08/12.45 % (1406346)Peak memory usage: 90 MB
% 70.08/12.45 % (1406346)Instructions burned: 257 (million)
% 70.08/12.45 % (1406362)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1333610228:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 70.08/12.45 % (1406365)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3107630231:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 70.08/12.45 % (1406365)Instruction limit reached!
% 70.08/12.45 % (1406365)------------------------------
% 70.08/12.45 % (1406365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406365)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406365)Termination reason: Instruction limit
% 70.08/12.45 % (1406365)Termination phase: Saturation
% 70.08/12.45 % (1406365)Time elapsed: 0.203 s
% 70.08/12.45 % (1406365)Peak memory usage: 92 MB
% 70.08/12.45 % (1406365)Instructions burned: 215 (million)
% 70.08/12.45 % (1406369)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1868471448:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2991 on theBenchmark for (2991ds/317Mi)
% 70.08/12.45 % (1406369)Instruction limit reached!
% 70.08/12.45 % (1406369)------------------------------
% 70.08/12.45 % (1406369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406369)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406369)Termination reason: Instruction limit
% 70.08/12.45 % (1406369)Termination phase: Saturation
% 70.08/12.45 % (1406369)Time elapsed: 0.178 s
% 70.08/12.45 % (1406369)Peak memory usage: 93 MB
% 70.08/12.45 % (1406369)Instructions burned: 319 (million)
% 70.08/12.45 % (1406347)Instruction limit reached!
% 70.08/12.45 % (1406347)------------------------------
% 70.08/12.45 % (1406347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406347)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406347)Termination reason: Instruction limit
% 70.08/12.45 % (1406347)Termination phase: Saturation
% 70.08/12.45 % (1406347)Time elapsed: 1.112 s
% 70.08/12.45 % (1406347)Peak memory usage: 99 MB
% 70.08/12.45 % (1406347)Instructions burned: 1187 (million)
% 70.08/12.45 % (1406375)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2644686314:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2987 on theBenchmark for (2987ds/12125Mi)
% 70.08/12.45 % (1406380)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1561725203:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2986 on theBenchmark for (2986ds/2836Mi)
% 70.08/12.45 % (1406355)Instruction limit reached!
% 70.08/12.45 % (1406355)------------------------------
% 70.08/12.45 % (1406355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406355)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406355)Termination reason: Instruction limit
% 70.08/12.45 % (1406355)Termination phase: Saturation
% 70.08/12.45 % (1406355)Time elapsed: 1.795 s
% 70.08/12.45 % (1406355)Peak memory usage: 142 MB
% 70.08/12.45 % (1406355)Instructions burned: 2051 (million)
% 70.08/12.45 % (1406385)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=2597830169:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2978 on theBenchmark for (2978ds/14534Mi)
% 70.08/12.45 % (1406380)Instruction limit reached!
% 70.08/12.45 % (1406380)------------------------------
% 70.08/12.45 % (1406380)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406380)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406380)Termination reason: Instruction limit
% 70.08/12.45 % (1406380)Termination phase: Saturation
% 70.08/12.45 % (1406380)Time elapsed: 1.558 s
% 70.08/12.45 % (1406380)Peak memory usage: 141 MB
% 70.08/12.45 % (1406380)Instructions burned: 2837 (million)
% 70.08/12.45 % (1406389)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=2992128530:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2969 on theBenchmark for (2969ds/11832Mi)
% 70.08/12.45 % (1406362)Instruction limit reached!
% 70.08/12.45 % (1406362)------------------------------
% 70.08/12.45 % (1406362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406362)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406362)Termination reason: Instruction limit
% 70.08/12.45 % (1406362)Termination phase: Saturation
% 70.08/12.45 % (1406362)Time elapsed: 4.967 s
% 70.08/12.45 % (1406362)Peak memory usage: 170 MB
% 70.08/12.45 % (1406362)Instructions burned: 4948 (million)
% 70.08/12.45 % (1406393)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=358732956:i=2279:fgj=on:bd=all_2944 on theBenchmark for (2944ds/2279Mi)
% 70.08/12.45 % (1406393)Instruction limit reached!
% 70.08/12.45 % (1406393)------------------------------
% 70.08/12.45 % (1406393)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406393)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406393)Termination reason: Instruction limit
% 70.08/12.45 % (1406393)Termination phase: Saturation
% 70.08/12.45 % (1406393)Time elapsed: 1.978 s
% 70.08/12.45 % (1406393)Peak memory usage: 140 MB
% 70.08/12.45 % (1406393)Instructions burned: 2279 (million)
% 70.08/12.45 % (1406446)lrs-1010_1_to=lpo:ncem=casc2026/models/loop8.pt:sil=32000:tgt=ground:npcc=on:drc=off:fde=none:sp=reverse_arity:urr=ec_only:gs=on:s2agt=16:random_seed=3882124709:st=3:i=6225:bd=all:gtg=exists_all:ss=included:er=filter:sgt=10_2922 on theBenchmark for (2922ds/6225Mi)
% 70.08/12.45 % (1406389)Instruction limit reached!
% 70.08/12.45 % (1406389)------------------------------
% 70.08/12.45 % (1406389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406389)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406389)Termination reason: Instruction limit
% 70.08/12.45 % (1406389)Termination phase: Saturation
% 70.08/12.45 % (1406389)Time elapsed: 5.701 s
% 70.08/12.45 % (1406389)Peak memory usage: 232 MB
% 70.08/12.45 % (1406389)Instructions burned: 11834 (million)
% 70.08/12.45 % (1406556)lrs-1010_1_sil=32000:tgt=ground:etr=on:sp=const_frequency:spb=goal_then_units:rnwc=on:lwlo=on:random_seed=1725534150:lrd=on:i=21755:kws=frequency:fgj=on:bd=preordered:nm=4:ins=20:av=off_2910 on theBenchmark for (2910ds/21755Mi)
% 70.08/12.45 % (1406375)Instruction limit reached!
% 70.08/12.45 % (1406375)------------------------------
% 70.08/12.45 % (1406375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 70.08/12.45 % (1406375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 70.08/12.45 % (1406375)CaDiCaL version: 2.1.3
% 70.08/12.45 % (1406375)Termination reason: Instruction limit
% 70.08/12.45 % (1406375)Termination phase: Saturation
% 70.08/12.45 % (1406375)Time elapsed: 9.716 s
% 70.08/12.45 % (1406375)Peak memory usage: 243 MB
% 70.08/12.45 % (1406375)Instructions burned: 12126 (million)
% 70.08/12.45 % (1406341)First to succeed.
% 70.08/12.45 % (1406341)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1406297"
% 70.08/12.45 % (1406558)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:drc=off:flr=on:random_seed=2437298390:s2pl=no:i=16427:s2at=1.5:bd=all:fsr=off_2888 on theBenchmark for (2888ds/16427Mi)
% 70.08/12.45 % (1406341)Refutation found. Thanks to Tanya!
% 70.08/12.45 % SZS status Unsatisfiable for theBenchmark
% 70.08/12.45 % SZS output start Proof for theBenchmark
% See solution above
% 82.52/12.64 % (1406341)------------------------------
% 82.52/12.64 % (1406341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 82.52/12.64 % (1406341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 82.52/12.64 % (1406341)CaDiCaL version: 2.1.3
% 82.52/12.64 % (1406341)Termination reason: Refutation
% 82.52/12.64 % (1406341)Time elapsed: 11.010 s
% 82.52/12.64 % (1406341)Peak memory usage: 260 MB
% 82.52/12.64 % (1406341)Instructions burned: 13312 (million)
% 82.52/12.64 % (1406341)------------------------------
% 82.52/12.64 % (1406341)------------------------------
% 82.52/12.64 % (1406297)Success in time 11.527 s
% 82.52/12.64 % Vampire exiting
%------------------------------------------------------------------------------