%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP167-1 : 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 : n011.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 18.14s 3.55s
% Output : Refutation 18.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 123 ( 55 unt; 11 def)
% Number of atoms : 245 ( 98 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 241 ( 119 ~; 114 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn 83 !; 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(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_lub) ).
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(f17,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_1) ).
fof(f18,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lat4_2) ).
fof(f21,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lat4) ).
fof(f22,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f21,f17,f18]) ).
fof(f23,definition,
sF0 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f24,plain,
least_upper_bound(a,identity) = sF0,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF1 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f26,plain,
greatest_lower_bound(a,identity) = sF1,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF2 = multiply(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f28,plain,
multiply(sF0,sF1) = sF2,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
a != sF2,
inference(definition_folding,[],[f22,f28,f26,f24]) ).
fof(f30,plain,
sF0 = least_upper_bound(identity,a),
inference(forward_demodulation,[],[f24,f6]) ).
fof(f31,plain,
sF1 = greatest_lower_bound(identity,a),
inference(forward_demodulation,[],[f26,f5]) ).
fof(f35,definition,
( spl3_1
<=> multiply(sF0,sF1) = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
fof(f37,plain,
( multiply(sF0,sF1) = sF2
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f38,plain,
spl3_1,
inference(avatar_split_clause,[],[f28,f35]) ).
fof(f40,definition,
( spl3_2
<=> sF1 = greatest_lower_bound(identity,a) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
fof(f42,plain,
( sF1 = greatest_lower_bound(identity,a)
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f43,plain,
spl3_2,
inference(avatar_split_clause,[],[f31,f40]) ).
fof(f44,plain,
( identity = least_upper_bound(identity,sF1)
| ~ spl3_2 ),
inference(superposition,[],[f11,f42]) ).
fof(f45,plain,
( identity = least_upper_bound(sF1,identity)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f44,f6]) ).
fof(f47,definition,
( spl3_3
<=> a = sF2 ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
fof(f49,plain,
( a != sF2
| spl3_3 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f29,f47]) ).
fof(f52,definition,
( spl3_4
<=> sF0 = least_upper_bound(identity,a) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
fof(f54,plain,
( sF0 = least_upper_bound(identity,a)
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
spl3_4,
inference(avatar_split_clause,[],[f30,f52]) ).
fof(f56,plain,
( identity = greatest_lower_bound(identity,sF0)
| ~ spl3_4 ),
inference(superposition,[],[f12,f54]) ).
fof(f57,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_4 ),
inference(forward_demodulation,[],[f56,f5]) ).
fof(f59,plain,
! [X0,X1] : least_upper_bound(X1,greatest_lower_bound(X0,X1)) = X1,
inference(superposition,[],[f11,f5]) ).
fof(f61,plain,
! [X0,X1] : greatest_lower_bound(X1,least_upper_bound(X0,X1)) = X1,
inference(superposition,[],[f12,f6]) ).
fof(f62,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X1),X0) = least_upper_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f15,f1]) ).
fof(f78,plain,
( ! [X0] : least_upper_bound(X0,multiply(a,X0)) = multiply(sF0,X0)
| ~ spl3_4 ),
inference(superposition,[],[f62,f54]) ).
fof(f93,plain,
! [X0,X1] : multiply(greatest_lower_bound(identity,X1),X0) = greatest_lower_bound(X0,multiply(X1,X0)),
inference(superposition,[],[f16,f1]) ).
fof(f111,plain,
( ! [X0] : greatest_lower_bound(X0,multiply(a,X0)) = multiply(sF1,X0)
| ~ spl3_2 ),
inference(superposition,[],[f93,f42]) ).
fof(f212,plain,
( a = least_upper_bound(a,sF1)
| ~ spl3_2 ),
inference(superposition,[],[f59,f42]) ).
fof(f220,plain,
( a = least_upper_bound(sF1,a)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f212,f6]) ).
fof(f230,plain,
( a = greatest_lower_bound(a,sF0)
| ~ spl3_4 ),
inference(superposition,[],[f61,f54]) ).
fof(f240,plain,
( a = greatest_lower_bound(sF0,a)
| ~ spl3_4 ),
inference(forward_demodulation,[],[f230,f5]) ).
fof(f248,plain,
! [X0,X1] : multiply(identity,X1) = multiply(inverse(X0),multiply(X0,X1)),
inference(superposition,[],[f4,f3]) ).
fof(f266,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(forward_demodulation,[],[f248,f1]) ).
fof(f279,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[],[f266,f3]) ).
fof(f280,plain,
! [X0,X1] : multiply(X1,X0) = multiply(inverse(inverse(X1)),X0),
inference(superposition,[],[f266,f266]) ).
fof(f300,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[],[f279,f280]) ).
fof(f481,plain,
( ! [X0] : multiply(a,greatest_lower_bound(X0,multiply(a,X0))) = multiply(sF1,multiply(a,X0))
| ~ spl3_2 ),
inference(superposition,[],[f14,f111]) ).
fof(f482,plain,
( ! [X0] : multiply(sF1,multiply(a,X0)) = multiply(a,multiply(sF1,X0))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f481,f111]) ).
fof(f653,plain,
( ! [X0] : least_upper_bound(sF0,X0) = least_upper_bound(identity,least_upper_bound(a,X0))
| ~ spl3_4 ),
inference(superposition,[],[f8,f54]) ).
fof(f655,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(f693,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(f747,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,[],[f693,f16]) ).
fof(f823,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,identity),multiply(greatest_lower_bound(X0,X1),a)) = greatest_lower_bound(multiply(X0,sF1),multiply(X1,a))
| ~ spl3_2 ),
inference(superposition,[],[f747,f42]) ).
fof(f949,plain,
( ! [X0,X1] : greatest_lower_bound(multiply(X0,sF1),multiply(X1,a)) = greatest_lower_bound(X0,multiply(greatest_lower_bound(X0,X1),a))
| ~ spl3_2 ),
inference(forward_demodulation,[],[f823,f300]) ).
fof(f1027,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,[],[f655,f15]) ).
fof(f1103,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,identity),multiply(least_upper_bound(X0,X1),a)) = least_upper_bound(multiply(X0,sF0),multiply(X1,a))
| ~ spl3_4 ),
inference(superposition,[],[f1027,f54]) ).
fof(f1229,plain,
( ! [X0,X1] : least_upper_bound(multiply(X0,sF0),multiply(X1,a)) = least_upper_bound(X0,multiply(least_upper_bound(X0,X1),a))
| ~ spl3_4 ),
inference(forward_demodulation,[],[f1103,f300]) ).
fof(f1819,plain,
( ! [X0] : multiply(X0,least_upper_bound(sF0,a)) = least_upper_bound(X0,multiply(least_upper_bound(X0,X0),a))
| ~ spl3_4 ),
inference(superposition,[],[f13,f1229]) ).
fof(f1860,plain,
( ! [X0] : multiply(X0,least_upper_bound(sF0,a)) = least_upper_bound(X0,multiply(X0,a))
| ~ spl3_4 ),
inference(forward_demodulation,[],[f1819,f9]) ).
fof(f1918,definition,
( spl3_5
<=> identity = greatest_lower_bound(sF0,identity) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
fof(f1920,plain,
( identity = greatest_lower_bound(sF0,identity)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f1918]) ).
fof(f1921,plain,
( spl3_5
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f57,f52,f1918]) ).
fof(f1930,plain,
( greatest_lower_bound(multiply(sF0,sF1),multiply(identity,a)) = greatest_lower_bound(sF0,multiply(identity,a))
| ~ spl3_2
| ~ spl3_5 ),
inference(superposition,[],[f949,f1920]) ).
fof(f1931,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(multiply(sF0,sF1),a)
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[],[f1930,f1]) ).
fof(f1938,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(a,multiply(sF0,sF1))
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[],[f1931,f5]) ).
fof(f1944,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(a,sF2)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[],[f1938,f37]) ).
fof(f1946,plain,
( greatest_lower_bound(sF0,a) = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_5 ),
inference(forward_demodulation,[],[f1944,f5]) ).
fof(f1948,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(forward_demodulation,[],[f1946,f240]) ).
fof(f1950,definition,
( spl3_6
<=> a = greatest_lower_bound(sF2,a) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
fof(f1952,plain,
( a = greatest_lower_bound(sF2,a)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f1953,plain,
( spl3_6
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f1948,f1918,f52,f40,f35,f1950]) ).
fof(f1955,plain,
( sF2 = least_upper_bound(sF2,a)
| ~ spl3_6 ),
inference(superposition,[],[f11,f1952]) ).
fof(f2046,definition,
( spl3_7
<=> identity = least_upper_bound(sF1,identity) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
fof(f2048,plain,
( identity = least_upper_bound(sF1,identity)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f2046]) ).
fof(f2049,plain,
( spl3_7
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f45,f40,f2046]) ).
fof(f2059,plain,
( least_upper_bound(multiply(sF1,sF0),multiply(identity,a)) = least_upper_bound(sF1,multiply(identity,a))
| ~ spl3_4
| ~ spl3_7 ),
inference(superposition,[],[f1229,f2048]) ).
fof(f2060,plain,
( least_upper_bound(sF1,a) = least_upper_bound(multiply(sF1,sF0),a)
| ~ spl3_4
| ~ spl3_7 ),
inference(forward_demodulation,[],[f2059,f1]) ).
fof(f2067,plain,
( least_upper_bound(sF1,a) = least_upper_bound(a,multiply(sF1,sF0))
| ~ spl3_4
| ~ spl3_7 ),
inference(forward_demodulation,[],[f2060,f6]) ).
fof(f2072,plain,
( a = least_upper_bound(a,multiply(sF1,sF0))
| ~ spl3_2
| ~ spl3_4
| ~ spl3_7 ),
inference(forward_demodulation,[],[f2067,f220]) ).
fof(f2151,plain,
( multiply(a,sF1) = multiply(sF1,multiply(a,identity))
| ~ spl3_2 ),
inference(superposition,[],[f482,f300]) ).
fof(f2179,plain,
( multiply(a,sF1) = multiply(sF1,a)
| ~ spl3_2 ),
inference(forward_demodulation,[],[f2151,f300]) ).
fof(f2260,plain,
( least_upper_bound(identity,a) = least_upper_bound(sF0,a)
| ~ spl3_4 ),
inference(superposition,[],[f653,f9]) ).
fof(f2286,plain,
( sF0 = least_upper_bound(sF0,a)
| ~ spl3_4 ),
inference(forward_demodulation,[],[f2260,f54]) ).
fof(f2291,plain,
( ! [X0] : multiply(X0,sF0) = least_upper_bound(X0,multiply(X0,a))
| ~ spl3_4 ),
inference(backward_demodulation,[],[f1860,f2286]) ).
fof(f3257,definition,
( spl3_11
<=> multiply(a,sF1) = multiply(sF1,a) ),
introduced(definition,[new_symbols(definition,[spl3_11])],[avatar_definition]) ).
fof(f3259,plain,
( multiply(a,sF1) = multiply(sF1,a)
| ~ spl3_11 ),
inference(avatar_component_clause,[],[f3257]) ).
fof(f3260,plain,
( spl3_11
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f2179,f40,f3257]) ).
fof(f3468,plain,
( multiply(sF0,sF1) = least_upper_bound(sF1,multiply(sF1,a))
| ~ spl3_4
| ~ spl3_11 ),
inference(superposition,[],[f78,f3259]) ).
fof(f3488,plain,
( multiply(sF0,sF1) = multiply(sF1,sF0)
| ~ spl3_4
| ~ spl3_11 ),
inference(forward_demodulation,[],[f3468,f2291]) ).
fof(f3489,plain,
( sF2 = multiply(sF1,sF0)
| ~ spl3_1
| ~ spl3_4
| ~ spl3_11 ),
inference(forward_demodulation,[],[f3488,f37]) ).
fof(f3491,plain,
( a = least_upper_bound(a,sF2)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_7
| ~ spl3_11 ),
inference(backward_demodulation,[],[f2072,f3489]) ).
fof(f3492,plain,
( a = least_upper_bound(sF2,a)
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_7
| ~ spl3_11 ),
inference(forward_demodulation,[],[f3491,f6]) ).
fof(f3493,plain,
( a = sF2
| ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_6
| ~ spl3_7
| ~ spl3_11 ),
inference(forward_demodulation,[],[f3492,f1955]) ).
fof(f3494,plain,
( $false
| ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4
| ~ spl3_6
| ~ spl3_7
| ~ spl3_11 ),
inference(forward_subsumption_resolution,[],[f3493,f49]) ).
fof(f3495,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4
| ~ spl3_6
| ~ spl3_7
| ~ spl3_11 ),
inference(avatar_contradiction_clause,[],[f3494]) ).
cnf(s1,plain,
spl3_1,
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
spl3_2,
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
~ spl3_3,
inference(sat_conversion,[],[f50]) ).
cnf(s4,plain,
spl3_4,
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
( ~ spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f1921]) ).
cnf(s6,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_4
| ~ spl3_5
| spl3_6 ),
inference(sat_conversion,[],[f1953]) ).
cnf(s7,plain,
( ~ spl3_2
| spl3_7 ),
inference(sat_conversion,[],[f2049]) ).
cnf(s11,plain,
( ~ spl3_2
| spl3_11 ),
inference(sat_conversion,[],[f3260]) ).
cnf(s13,plain,
( ~ spl3_1
| ~ spl3_2
| spl3_3
| ~ spl3_4
| ~ spl3_6
| ~ spl3_7
| ~ spl3_11 ),
inference(sat_conversion,[],[f3495]) ).
cnf(s15,plain,
spl3_5,
inference(rat,[],[s5,s4]) ).
cnf(s16,plain,
spl3_11,
inference(rat,[],[s11,s2]) ).
cnf(s17,plain,
spl3_7,
inference(rat,[],[s7,s2]) ).
cnf(s18,plain,
~ spl3_6,
inference(rat,[],[s13,s16,s17,s2,s4,s3,s1]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s6,s2,s15,s4,s18,s1]) ).
fof(f3496,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 09:34:45 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 18.14/3.55 % (2150310)Detected a unit-equality problem, will run specialized UEQ schedule.
% 18.14/3.55 % (2150321)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=705512406:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 18.14/3.55 % (2150318)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4045617348:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 18.14/3.55 % (2150316)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=595622218:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 18.14/3.55 % (2150317)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2896210456:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 18.14/3.55 % (2150320)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=557101751:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 18.14/3.55 % (2150319)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1762531249:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 18.14/3.55 % (2150315)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=2151606399:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 18.14/3.55 % (2150318)Instruction limit reached!
% 18.14/3.55 % (2150318)------------------------------
% 18.14/3.55 % (2150318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150318)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150318)Termination reason: Instruction limit
% 18.14/3.55 % (2150318)Termination phase: Saturation
% 18.14/3.55 % (2150318)Time elapsed: 0.137 s
% 18.14/3.55 % (2150318)Peak memory usage: 88 MB
% 18.14/3.55 % (2150318)Instructions burned: 136 (million)
% 18.14/3.55 % (2150319)Instruction limit reached!
% 18.14/3.55 % (2150319)------------------------------
% 18.14/3.55 % (2150319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150319)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150319)Termination reason: Instruction limit
% 18.14/3.55 % (2150319)Termination phase: Saturation
% 18.14/3.55 % (2150319)Time elapsed: 0.178 s
% 18.14/3.55 % (2150319)Peak memory usage: 89 MB
% 18.14/3.55 % (2150319)Instructions burned: 181 (million)
% 18.14/3.55 % (2150320)Instruction limit reached!
% 18.14/3.55 % (2150320)------------------------------
% 18.14/3.55 % (2150320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150320)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150320)Termination reason: Instruction limit
% 18.14/3.55 % (2150320)Termination phase: Saturation
% 18.14/3.55 % (2150320)Time elapsed: 0.261 s
% 18.14/3.55 % (2150320)Peak memory usage: 90 MB
% 18.14/3.55 % (2150320)Instructions burned: 257 (million)
% 18.14/3.55 % (2150329)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2577862516:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 18.14/3.55 % (2150330)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3018998305:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 18.14/3.55 % (2150331)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1072684980:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 18.14/3.55 % (2150331)Instruction limit reached!
% 18.14/3.55 % (2150331)------------------------------
% 18.14/3.55 % (2150331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150331)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150331)Termination reason: Instruction limit
% 18.14/3.55 % (2150331)Termination phase: Saturation
% 18.14/3.55 % (2150331)Time elapsed: 0.191 s
% 18.14/3.55 % (2150331)Peak memory usage: 91 MB
% 18.14/3.55 % (2150331)Instructions burned: 215 (million)
% 18.14/3.55 % (2150321)Instruction limit reached!
% 18.14/3.55 % (2150321)------------------------------
% 18.14/3.55 % (2150321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150321)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150321)Termination reason: Instruction limit
% 18.14/3.55 % (2150321)Termination phase: Saturation
% 18.14/3.55 % (2150321)Time elapsed: 0.937 s
% 18.14/3.55 % (2150321)Peak memory usage: 99 MB
% 18.14/3.55 % (2150321)Instructions burned: 1188 (million)
% 18.14/3.55 % (2150335)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=2029928787:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2989 on theBenchmark for (2989ds/317Mi)
% 18.14/3.55 % (2150336)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=55628246:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2988 on theBenchmark for (2988ds/12125Mi)
% 18.14/3.55 % (2150335)Instruction limit reached!
% 18.14/3.55 % (2150335)------------------------------
% 18.14/3.55 % (2150335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150335)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150335)Termination reason: Instruction limit
% 18.14/3.55 % (2150335)Termination phase: Saturation
% 18.14/3.55 % (2150335)Time elapsed: 0.299 s
% 18.14/3.55 % (2150335)Peak memory usage: 90 MB
% 18.14/3.55 % (2150335)Instructions burned: 317 (million)
% 18.14/3.55 % (2150329)Instruction limit reached!
% 18.14/3.55 % (2150329)------------------------------
% 18.14/3.55 % (2150329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.14/3.55 % (2150329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.14/3.55 % (2150329)CaDiCaL version: 2.1.3
% 18.14/3.55 % (2150329)Termination reason: Instruction limit
% 18.14/3.55 % (2150329)Termination phase: Saturation
% 18.14/3.55 % (2150329)Time elapsed: 1.216 s
% 18.14/3.55 % (2150329)Peak memory usage: 143 MB
% 18.14/3.55 % (2150329)Instructions burned: 2051 (million)
% 18.14/3.55 % (2150339)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2326868:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2984 on theBenchmark for (2984ds/2836Mi)
% 18.14/3.55 % (2150315)First to succeed.
% 18.14/3.55 % (2150340)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=809964637:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2981 on theBenchmark for (2981ds/14534Mi)
% 18.14/3.55 % (2150315)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2150310"
% 18.14/3.55 % (2150317)Also succeeded, but the first one will report.
% 18.14/3.55 % (2150315)Refutation found. Thanks to Tanya!
% 18.14/3.55 % SZS status Unsatisfiable for theBenchmark
% 18.14/3.55 % SZS output start Proof for theBenchmark
% See solution above
% 18.66/3.79 % (2150315)------------------------------
% 18.66/3.79 % (2150315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 18.66/3.79 % (2150315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 18.66/3.79 % (2150315)CaDiCaL version: 2.1.3
% 18.66/3.79 % (2150315)Termination reason: Refutation
% 18.66/3.79 % (2150315)Time elapsed: 1.820 s
% 18.66/3.79 % (2150315)Peak memory usage: 137 MB
% 18.66/3.79 % (2150315)Instructions burned: 1675 (million)
% 18.66/3.79 % (2150315)------------------------------
% 18.66/3.79 % (2150315)------------------------------
% 18.66/3.79 % (2150310)Success in time 2.534 s
% 18.66/3.79 % Vampire exiting
%------------------------------------------------------------------------------