%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 10:13:08 AM UTC 2026
% Result : Unsatisfiable 5.95s 1.93s
% Output : Refutation 8.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 35
% Syntax : Number of formulae : 175 ( 68 unt; 17 def)
% Number of atoms : 377 ( 132 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 394 ( 192 ~; 188 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
fof(f21,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
fof(f22,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_5) ).
fof(f25,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
fof(f26,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f25,f21,f22]) ).
fof(f27,definition,
sF0 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f28,plain,
least_upper_bound(a,identity) = sF0,
inference(reorient_equations,[],[f27]) ).
fof(f29,definition,
sF1 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f30,plain,
greatest_lower_bound(a,identity) = sF1,
inference(reorient_equations,[],[f29]) ).
fof(f31,definition,
sF2 = multiply(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f32,plain,
multiply(sF0,sF1) = sF2,
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
a != sF2,
inference(definition_folding,[],[f26,f32,f30,f28]) ).
fof(f34,plain,
sF0 = least_upper_bound(identity,a),
inference(forward_demodulation,[],[f28,f6]) ).
fof(f35,plain,
sF1 = greatest_lower_bound(identity,a),
inference(forward_demodulation,[],[f30,f5]) ).
fof(f39,definition,
( spl3_1
<=> multiply(sF0,sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f41,plain,
( multiply(sF0,sF1) = sF2
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
spl3_1,
inference(avatar_split_clause,[],[f32,f39]) ).
fof(f44,definition,
( spl3_2
<=> a = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f46,plain,
( a != sF2
| spl3_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
~ spl3_2,
inference(avatar_split_clause,[],[f33,f44]) ).
fof(f49,definition,
( spl3_3
<=> sF1 = greatest_lower_bound(identity,a) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f51,plain,
( sF1 = greatest_lower_bound(identity,a)
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f52,plain,
spl3_3,
inference(avatar_split_clause,[],[f35,f49]) ).
fof(f53,plain,
( identity = least_upper_bound(identity,sF1)
| ~ spl3_3 ),
inference(superposition,[],[f11,f51]) ).
fof(f54,plain,
( identity = least_upper_bound(sF1,identity)
| ~ spl3_3 ),
inference(forward_demodulation,[],[f53,f6]) ).
fof(f56,definition,
( spl3_4
<=> sF0 = least_upper_bound(identity,a) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f58,plain,
( sF0 = least_upper_bound(identity,a)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f56]) ).
fof(f59,plain,
spl3_4,
inference(avatar_split_clause,[],[f34,f56]) ).
fof(f60,plain,
( identity = greatest_lower_bound(identity,sF0)
| ~ spl3_4 ),
inference(superposition,[],[f12,f58]) ).
fof(f61,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_4 ),
inference(forward_demodulation,[],[f60,f5]) ).
fof(f63,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f65,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f66,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f82,plain,
( ! [X0] : least_upper_bound(X0,multiply(a,X0)) = multiply(sF0,X0)
| ~ spl3_4 ),
inference(superposition,[],[f66,f58]) ).
fof(f97,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f115,plain,
( ! [X0] : greatest_lower_bound(X0,multiply(a,X0)) = multiply(sF1,X0)
| ~ spl3_3 ),
inference(superposition,[],[f97,f51]) ).
fof(f142,plain,
( a = least_upper_bound(a,sF1)
| ~ spl3_3 ),
inference(superposition,[],[f63,f51]) ).
fof(f148,plain,
( a = least_upper_bound(sF1,a)
| ~ spl3_3 ),
inference(forward_demodulation,[],[f142,f6]) ).
fof(f156,plain,
( ! [X0] : multiply(sF0,greatest_lower_bound(sF1,X0)) = greatest_lower_bound(sF2,multiply(sF0,X0))
| ~ spl3_1 ),
inference(superposition,[],[f14,f41]) ).
fof(f215,plain,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[],[f6,f13]) ).
fof(f218,plain,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = multiply(X0,least_upper_bound(X2,X1)),
inference(forward_demodulation,[],[f215,f13]) ).
fof(f234,plain,
( a = greatest_lower_bound(a,sF0)
| ~ spl3_4 ),
inference(superposition,[],[f65,f58]) ).
fof(f244,plain,
( a = greatest_lower_bound(sF0,a)
| ~ spl3_4 ),
inference(forward_demodulation,[],[f234,f5]) ).
fof(f252,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f255,plain,
( ! [X0] : multiply(sF0,multiply(sF1,X0)) = multiply(sF2,X0)
| ~ spl3_1 ),
inference(superposition,[],[f4,f41]) ).
fof(f270,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f252,f1]) ).
fof(f283,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f270,f3]) ).
fof(f304,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f283,f19]) ).
fof(f439,plain,
( ! [X0] : multiply(a,least_upper_bound(X0,multiply(a,X0))) = multiply(sF0,multiply(a,X0))
| ~ spl3_4 ),
inference(superposition,[],[f13,f82]) ).
fof(f440,plain,
( ! [X0] : multiply(sF0,multiply(a,X0)) = multiply(a,multiply(sF0,X0))
| ~ spl3_4 ),
inference(forward_demodulation,[],[f439,f82]) ).
fof(f458,plain,
( ! [X0] : multiply(a,greatest_lower_bound(X0,multiply(a,X0))) = multiply(sF1,multiply(a,X0))
| ~ spl3_3 ),
inference(superposition,[],[f14,f115]) ).
fof(f459,plain,
( ! [X0] : multiply(sF1,multiply(a,X0)) = multiply(a,multiply(sF1,X0))
| ~ spl3_3 ),
inference(forward_demodulation,[],[f458,f115]) ).
fof(f582,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,X1),least_upper_bound(multiply(X0,X2),X3)) = least_upper_bound(multiply(X0,least_upper_bound(X1,X2)),X3),
inference(superposition,[],[f8,f13]) ).
fof(f659,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = inverse(multiply(X1,inverse(X0))),
inference(superposition,[],[f20,f19]) ).
fof(f678,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(inverse(X1)),inverse(multiply(X0,X1))),
inference(superposition,[],[f270,f20]) ).
fof(f679,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(multiply(X0,X1),inverse(X1))),
inference(forward_demodulation,[],[f678,f20]) ).
fof(f686,plain,
! [X0,X1] : inverse(X0) = multiply(X1,inverse(multiply(X0,X1))),
inference(forward_demodulation,[],[f679,f659]) ).
fof(f692,plain,
( greatest_lower_bound(sF2,multiply(sF0,multiply(a,sF1))) = multiply(sF0,multiply(sF1,sF1))
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[],[f156,f115]) ).
fof(f710,plain,
( greatest_lower_bound(sF2,multiply(sF0,multiply(a,sF1))) = multiply(sF2,sF1)
| ~ spl3_1
| ~ spl3_3 ),
inference(forward_demodulation,[],[f692,f255]) ).
fof(f728,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(f928,plain,
! [X2,X3,X0,X1] : least_upper_bound(multiply(X0,least_upper_bound(X3,X2)),multiply(X1,X2)) = least_upper_bound(multiply(X0,X3),multiply(least_upper_bound(X0,X1),X2)),
inference(superposition,[],[f582,f15]) ).
fof(f1376,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,[],[f728,f16]) ).
fof(f1942,definition,
( spl3_7
<=> identity = greatest_lower_bound(sF0,identity) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f1944,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f1945,plain,
( spl3_7
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f61,f56,f1942]) ).
fof(f1953,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(sF0,greatest_lower_bound(X0,X1)),multiply(identity,X1)) = greatest_lower_bound(multiply(sF0,X0),multiply(identity,X1))
| ~ spl3_7 ),
inference(superposition,[],[f1376,f1944]) ).
fof(f1956,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(sF0,X0),X1) = greatest_lower_bound(multiply(sF0,greatest_lower_bound(X0,X1)),X1)
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1953,f1]) ).
fof(f1963,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(sF0,X0),X1) = greatest_lower_bound(X1,multiply(sF0,greatest_lower_bound(X0,X1)))
| ~ spl3_7 ),
inference(forward_demodulation,[],[f1956,f5]) ).
fof(f2053,plain,
( multiply(sF0,multiply(a,sF1)) = multiply(a,sF2)
| ~ spl3_1
| ~ spl3_4 ),
inference(superposition,[],[f440,f41]) ).
fof(f2087,plain,
( multiply(sF2,sF1) = greatest_lower_bound(sF2,multiply(a,sF2))
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[],[f710,f2053]) ).
fof(f2092,plain,
( multiply(sF2,sF1) = multiply(sF1,sF2)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_demodulation,[],[f2087,f115]) ).
fof(f2094,plain,
( multiply(a,sF1) = multiply(sF1,multiply(a,identity))
| ~ spl3_3 ),
inference(superposition,[],[f459,f304]) ).
fof(f2124,plain,
( multiply(a,sF1) = multiply(sF1,a)
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2094,f304]) ).
fof(f2129,plain,
( multiply(a,sF2) = multiply(sF0,multiply(sF1,a))
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(backward_demodulation,[],[f2053,f2124]) ).
fof(f2132,plain,
( multiply(a,sF2) = multiply(sF2,a)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_demodulation,[],[f2129,f255]) ).
fof(f2134,definition,
( spl3_9
<=> multiply(a,sF2) = multiply(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition]) ).
fof(f2136,plain,
( multiply(a,sF2) = multiply(sF2,a)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f2134]) ).
fof(f2137,plain,
( spl3_9
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f2132,f56,f49,f39,f2134]) ).
fof(f2149,plain,
( sF2 = multiply(inverse(a),multiply(sF2,a))
| ~ spl3_9 ),
inference(superposition,[],[f270,f2136]) ).
fof(f2267,definition,
( spl3_10
<=> identity = least_upper_bound(sF1,identity) ),
introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition]) ).
fof(f2269,plain,
( identity = least_upper_bound(sF1,identity)
| ~ spl3_10 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f2270,plain,
( spl3_10
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f54,f49,f2267]) ).
fof(f2279,plain,
( ! [X0,X1] : least_upper_bound(multiply(sF1,least_upper_bound(X0,X1)),multiply(identity,X1)) = least_upper_bound(multiply(sF1,X0),multiply(identity,X1))
| ~ spl3_10 ),
inference(superposition,[],[f928,f2269]) ).
fof(f2282,plain,
( ! [X0,X1] : least_upper_bound(multiply(sF1,X0),X1) = least_upper_bound(multiply(sF1,least_upper_bound(X0,X1)),X1)
| ~ spl3_10 ),
inference(forward_demodulation,[],[f2279,f1]) ).
fof(f2289,plain,
( ! [X0,X1] : least_upper_bound(multiply(sF1,X0),X1) = least_upper_bound(X1,multiply(sF1,least_upper_bound(X0,X1)))
| ~ spl3_10 ),
inference(forward_demodulation,[],[f2282,f6]) ).
fof(f2984,plain,
! [X2,X0,X1] : inverse(multiply(X0,X1)) = multiply(X2,inverse(multiply(X0,multiply(X1,X2)))),
inference(superposition,[],[f686,f4]) ).
fof(f2999,plain,
( ! [X0] : inverse(a) = multiply(multiply(sF1,X0),inverse(multiply(sF1,multiply(a,X0))))
| ~ spl3_3 ),
inference(superposition,[],[f686,f459]) ).
fof(f3071,plain,
( ! [X0] : inverse(a) = multiply(sF1,multiply(X0,inverse(multiply(sF1,multiply(a,X0)))))
| ~ spl3_3 ),
inference(forward_demodulation,[],[f2999,f4]) ).
fof(f3096,plain,
( inverse(a) = multiply(sF1,inverse(multiply(sF1,a)))
| ~ spl3_3 ),
inference(forward_demodulation,[],[f3071,f2984]) ).
fof(f4519,definition,
( spl3_16
<=> multiply(a,sF1) = multiply(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl3_16])],[avatar_definition]) ).
fof(f4521,plain,
( multiply(a,sF1) = multiply(sF1,a)
| ~ spl3_16 ),
inference(avatar_component_clause,[],[f4519]) ).
fof(f4522,plain,
( spl3_16
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f2124,f49,f4519]) ).
fof(f4524,plain,
( multiply(sF0,sF1) = least_upper_bound(sF1,multiply(sF1,a))
| ~ spl3_4
| ~ spl3_16 ),
inference(superposition,[],[f82,f4521]) ).
fof(f4552,plain,
( sF2 = least_upper_bound(sF1,multiply(sF1,a))
| ~ spl3_1
| ~ spl3_4
| ~ spl3_16 ),
inference(forward_demodulation,[],[f4524,f41]) ).
fof(f4562,definition,
( spl3_18
<=> multiply(sF2,sF1) = multiply(sF1,sF2) ),
introduced(definition,[new_symbols(definition,[spl3_18])],[avatar_definition]) ).
fof(f4564,plain,
( multiply(sF2,sF1) = multiply(sF1,sF2)
| ~ spl3_18 ),
inference(avatar_component_clause,[],[f4562]) ).
fof(f4565,plain,
( spl3_18
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f2092,f56,f49,f39,f4562]) ).
fof(f4582,plain,
( inverse(sF2) = multiply(sF1,inverse(multiply(sF1,sF2)))
| ~ spl3_18 ),
inference(superposition,[],[f686,f4564]) ).
fof(f4676,definition,
( spl3_22
<=> a = greatest_lower_bound(sF0,a) ),
introduced(definition,[new_symbols(definition,[spl3_22])],[avatar_definition]) ).
fof(f4678,plain,
( a = greatest_lower_bound(sF0,a)
| ~ spl3_22 ),
inference(avatar_component_clause,[],[f4676]) ).
fof(f4679,plain,
( spl3_22
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f244,f56,f4676]) ).
fof(f4713,plain,
( greatest_lower_bound(multiply(sF0,identity),a) = greatest_lower_bound(a,multiply(sF0,sF1))
| ~ spl3_3
| ~ spl3_7 ),
inference(superposition,[],[f1963,f51]) ).
fof(f4795,plain,
( greatest_lower_bound(multiply(sF0,identity),a) = greatest_lower_bound(a,sF2)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f4713,f41]) ).
fof(f4818,plain,
( greatest_lower_bound(multiply(sF0,identity),a) = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f4795,f5]) ).
fof(f4829,plain,
( greatest_lower_bound(sF2,a) = greatest_lower_bound(a,multiply(sF0,identity))
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f4818,f5]) ).
fof(f4837,plain,
( greatest_lower_bound(a,sF0) = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f4829,f304]) ).
fof(f4843,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7 ),
inference(forward_demodulation,[],[f4837,f5]) ).
fof(f4849,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7
| ~ spl3_22 ),
inference(forward_demodulation,[],[f4843,f4678]) ).
fof(f4853,definition,
( spl3_23
<=> a = greatest_lower_bound(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_23])],[avatar_definition]) ).
fof(f4855,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f4853]) ).
fof(f4856,plain,
( spl3_23
| ~ spl3_1
| ~ spl3_3
| ~ spl3_7
| ~ spl3_22 ),
inference(avatar_split_clause,[],[f4849,f4676,f1942,f49,f39,f4853]) ).
fof(f4858,plain,
( sF2 = least_upper_bound(sF2,a)
| ~ spl3_23 ),
inference(superposition,[],[f11,f4855]) ).
fof(f4879,definition,
( spl3_24
<=> sF2 = least_upper_bound(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_24])],[avatar_definition]) ).
fof(f4881,plain,
( sF2 = least_upper_bound(sF2,a)
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f4879]) ).
fof(f4882,plain,
( spl3_24
| ~ spl3_23 ),
inference(avatar_split_clause,[],[f4858,f4853,f4879]) ).
fof(f5241,definition,
( spl3_26
<=> a = least_upper_bound(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl3_26])],[avatar_definition]) ).
fof(f5243,plain,
( a = least_upper_bound(sF1,a)
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f5241]) ).
fof(f5244,plain,
( spl3_26
| ~ spl3_3 ),
inference(avatar_split_clause,[],[f148,f49,f5241]) ).
fof(f6523,definition,
( spl3_27
<=> sF2 = least_upper_bound(sF1,multiply(sF1,a)) ),
introduced(definition,[new_symbols(definition,[spl3_27])],[avatar_definition]) ).
fof(f6525,plain,
( sF2 = least_upper_bound(sF1,multiply(sF1,a))
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f6523]) ).
fof(f6526,plain,
( spl3_27
| ~ spl3_1
| ~ spl3_4
| ~ spl3_16 ),
inference(avatar_split_clause,[],[f4552,f4519,f56,f39,f6523]) ).
fof(f6541,plain,
( least_upper_bound(multiply(sF1,sF1),multiply(sF1,a)) = least_upper_bound(multiply(sF1,a),multiply(sF1,sF2))
| ~ spl3_10
| ~ spl3_27 ),
inference(superposition,[],[f2289,f6525]) ).
fof(f6542,plain,
( least_upper_bound(multiply(sF1,sF1),multiply(sF1,a)) = multiply(sF1,least_upper_bound(a,sF2))
| ~ spl3_10
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6541,f13]) ).
fof(f6551,plain,
( multiply(sF1,least_upper_bound(sF2,a)) = least_upper_bound(multiply(sF1,sF1),multiply(sF1,a))
| ~ spl3_10
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6542,f218]) ).
fof(f6556,plain,
( multiply(sF1,least_upper_bound(sF2,a)) = multiply(sF1,least_upper_bound(sF1,a))
| ~ spl3_10
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6551,f13]) ).
fof(f6561,plain,
( multiply(sF1,a) = multiply(sF1,least_upper_bound(sF2,a))
| ~ spl3_10
| ~ spl3_26
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6556,f5243]) ).
fof(f6565,plain,
( multiply(sF1,sF2) = multiply(sF1,a)
| ~ spl3_10
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6561,f4881]) ).
fof(f6568,plain,
( inverse(a) = multiply(sF1,inverse(multiply(sF1,sF2)))
| ~ spl3_3
| ~ spl3_10
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(backward_demodulation,[],[f3096,f6565]) ).
fof(f6605,plain,
( inverse(a) = inverse(sF2)
| ~ spl3_3
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6568,f4582]) ).
fof(f6612,plain,
( sF2 = multiply(inverse(sF2),multiply(sF2,a))
| ~ spl3_3
| ~ spl3_9
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(backward_demodulation,[],[f2149,f6605]) ).
fof(f6694,plain,
( a = sF2
| ~ spl3_3
| ~ spl3_9
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(forward_demodulation,[],[f6612,f270]) ).
fof(f6707,plain,
( $false
| spl3_2
| ~ spl3_3
| ~ spl3_9
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(forward_subsumption_resolution,[],[f6694,f46]) ).
fof(f6708,plain,
( spl3_2
| ~ spl3_3
| ~ spl3_9
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(avatar_contradiction_clause,[],[f6707]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
~ spl3_2,
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
spl3_3,
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
spl3_4,
inference(sat_conversion,[],[f59]) ).
cnf(s7,plain,
( ~ spl3_4
| spl3_7 ),
inference(sat_conversion,[],[f1945]) ).
cnf(s9,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4
| spl3_9 ),
inference(sat_conversion,[],[f2137]) ).
cnf(s10,plain,
( ~ spl3_3
| spl3_10 ),
inference(sat_conversion,[],[f2270]) ).
cnf(s16,plain,
( ~ spl3_3
| spl3_16 ),
inference(sat_conversion,[],[f4522]) ).
cnf(s18,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4
| spl3_18 ),
inference(sat_conversion,[],[f4565]) ).
cnf(s22,plain,
( ~ spl3_4
| spl3_22 ),
inference(sat_conversion,[],[f4679]) ).
cnf(s23,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_7
| ~ spl3_22
| spl3_23 ),
inference(sat_conversion,[],[f4856]) ).
cnf(s24,plain,
( ~ spl3_23
| spl3_24 ),
inference(sat_conversion,[],[f4882]) ).
cnf(s26,plain,
( ~ spl3_3
| spl3_26 ),
inference(sat_conversion,[],[f5244]) ).
cnf(s27,plain,
( ~ spl3_1
| ~ spl3_4
| ~ spl3_16
| spl3_27 ),
inference(sat_conversion,[],[f6526]) ).
cnf(s28,plain,
( spl3_2
| ~ spl3_3
| ~ spl3_9
| ~ spl3_10
| ~ spl3_18
| ~ spl3_24
| ~ spl3_26
| ~ spl3_27 ),
inference(sat_conversion,[],[f6708]) ).
cnf(s29,plain,
spl3_22,
inference(rat,[],[s22,s4]) ).
cnf(s31,plain,
spl3_7,
inference(rat,[],[s7,s4]) ).
cnf(s35,plain,
spl3_26,
inference(rat,[],[s26,s3]) ).
cnf(s36,plain,
spl3_16,
inference(rat,[],[s16,s3]) ).
cnf(s37,plain,
spl3_10,
inference(rat,[],[s10,s3]) ).
cnf(s42,plain,
spl3_27,
inference(rat,[],[s27,s36,s4,s1]) ).
cnf(s43,plain,
spl3_23,
inference(rat,[],[s23,s3,s29,s31,s1]) ).
cnf(s44,plain,
spl3_18,
inference(rat,[],[s18,s3,s4,s1]) ).
cnf(s47,plain,
spl3_9,
inference(rat,[],[s9,s3,s4,s1]) ).
cnf(s48,plain,
spl3_24,
inference(rat,[],[s24,s43]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s28,s42,s35,s48,s2,s37,s3,s44,s47]) ).
fof(f6716,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:39:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.95/1.92 % (2366648)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.95/1.92 % (2366653)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=1776427592:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.95/1.92 % (2366659)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=619650844:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.95/1.92 % (2366655)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2444449971:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.95/1.92 % (2366654)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=3583687409:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.95/1.92 % (2366657)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=356304545:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.95/1.93 % (2366656)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2650761532:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.95/1.93 % (2366658)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3825893555:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.95/1.93 % (2366656)Instruction limit reached!
% 5.95/1.93 % (2366656)------------------------------
% 5.95/1.93 % (2366656)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366656)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366656)Termination reason: Instruction limit
% 5.95/1.93 % (2366656)Termination phase: Saturation
% 5.95/1.93 % (2366656)Time elapsed: 0.080 s
% 5.95/1.93 % (2366656)Peak memory usage: 88 MB
% 5.95/1.93 % (2366656)Instructions burned: 136 (million)
% 5.95/1.93 % (2366657)Instruction limit reached!
% 5.95/1.93 % (2366657)------------------------------
% 5.95/1.93 % (2366657)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366657)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366657)Termination reason: Instruction limit
% 5.95/1.93 % (2366657)Termination phase: Saturation
% 5.95/1.93 % (2366657)Time elapsed: 0.109 s
% 5.95/1.93 % (2366657)Peak memory usage: 89 MB
% 5.95/1.93 % (2366657)Instructions burned: 183 (million)
% 5.95/1.93 % (2366658)Instruction limit reached!
% 5.95/1.93 % (2366658)------------------------------
% 5.95/1.93 % (2366658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366658)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366658)Termination reason: Instruction limit
% 5.95/1.93 % (2366658)Termination phase: Saturation
% 5.95/1.93 % (2366658)Time elapsed: 0.161 s
% 5.95/1.93 % (2366658)Peak memory usage: 90 MB
% 5.95/1.93 % (2366658)Instructions burned: 258 (million)
% 5.95/1.93 % (2366667)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1248359159:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 5.95/1.93 % (2366668)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=4257487288:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 5.95/1.93 % (2366669)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1343343476:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 5.95/1.93 % (2366669)Instruction limit reached!
% 5.95/1.93 % (2366669)------------------------------
% 5.95/1.93 % (2366669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366669)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366669)Termination reason: Instruction limit
% 5.95/1.93 % (2366669)Termination phase: Saturation
% 5.95/1.93 % (2366669)Time elapsed: 0.110 s
% 5.95/1.93 % (2366669)Peak memory usage: 91 MB
% 5.95/1.93 % (2366669)Instructions burned: 217 (million)
% 5.95/1.93 % (2366673)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=4213819597:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 5.95/1.93 % (2366659)Instruction limit reached!
% 5.95/1.93 % (2366659)------------------------------
% 5.95/1.93 % (2366659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366659)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366659)Termination reason: Instruction limit
% 5.95/1.93 % (2366659)Termination phase: Saturation
% 5.95/1.93 % (2366659)Time elapsed: 0.649 s
% 5.95/1.93 % (2366659)Peak memory usage: 99 MB
% 5.95/1.93 % (2366659)Instructions burned: 1189 (million)
% 5.95/1.93 % (2366653)First to succeed.
% 5.95/1.93 % (2366653)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2366648"
% 5.95/1.93 % (2366673)Instruction limit reached!
% 5.95/1.93 % (2366673)------------------------------
% 5.95/1.93 % (2366673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.93 % (2366673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.93 % (2366673)CaDiCaL version: 2.1.3
% 5.95/1.93 % (2366673)Termination reason: Instruction limit
% 5.95/1.93 % (2366673)Termination phase: Saturation
% 5.95/1.93 % (2366673)Time elapsed: 0.197 s
% 5.95/1.93 % (2366673)Peak memory usage: 93 MB
% 5.95/1.93 % (2366673)Instructions burned: 318 (million)
% 5.95/1.93 % (2366675)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=4089671802:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 5.95/1.93 % (2366653)Refutation found. Thanks to Tanya!
% 5.95/1.93 % SZS status Unsatisfiable for theBenchmark
% 5.95/1.93 % SZS output start Proof for theBenchmark
% See solution above
% 8.02/2.12 % (2366653)------------------------------
% 8.02/2.12 % (2366653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.02/2.12 % (2366653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.02/2.12 % (2366653)CaDiCaL version: 2.1.3
% 8.02/2.12 % (2366653)Termination reason: Refutation
% 8.02/2.12 % (2366653)Time elapsed: 0.767 s
% 8.02/2.12 % (2366653)Peak memory usage: 143 MB
% 8.02/2.12 % (2366653)Instructions burned: 2192 (million)
% 8.02/2.12 % (2366653)------------------------------
% 8.02/2.12 % (2366653)------------------------------
% 8.02/2.12 % (2366648)Success in time 1.055 s
% 8.02/2.12 % Vampire exiting
%------------------------------------------------------------------------------