%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:32:14 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 23
% Syntax : Number of formulae : 108 ( 53 unt; 0 def)
% Number of atoms : 279 ( 87 equ)
% Maximal formula atoms : 21 ( 2 avg)
% Number of connectives : 314 ( 143 ~; 112 |; 44 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-1 aty)
% Number of variables : 75 ( 71 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( X0 = monday
| X0 = tuesday
| X0 = wednesday
| X0 = thursday
| X0 = friday
| X0 = saturday
| X0 = sunday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',days_of_week) ).
fof(f2,axiom,
( monday != tuesday
& monday != wednesday
& monday != thursday
& monday != friday
& monday != saturday
& monday != sunday
& tuesday != wednesday
& tuesday != thursday
& tuesday != friday
& tuesday != saturday
& tuesday != sunday
& wednesday != thursday
& wednesday != friday
& wednesday != saturday
& wednesday != sunday
& thursday != friday
& thursday != saturday
& thursday != sunday
& friday != saturday
& friday != sunday
& saturday != sunday ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniquenames) ).
fof(f3,axiom,
! [X0,X1] :
( ( truthday(X0)
& truthday(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truth_unique) ).
fof(f4,axiom,
! [X0,X1] :
( ( day1(X0)
& day1(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day1_unique) ).
fof(f5,axiom,
! [X0,X1] :
( ( day2(X0)
& day2(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_unique) ).
fof(f6,axiom,
! [X0,X1] :
( ( day3(X0)
& day3(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_unique) ).
fof(f7,axiom,
? [X0] : truthday(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truth_once) ).
fof(f8,axiom,
? [X0] : day1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day1_once) ).
fof(f9,axiom,
? [X0] : day2(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_once) ).
fof(f10,axiom,
? [X0] : day3(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_once) ).
fof(f11,axiom,
consecutive(sunday) = monday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monday_follows_sunday) ).
fof(f12,axiom,
consecutive(monday) = tuesday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuesday_follows_monday) ).
fof(f13,axiom,
consecutive(tuesday) = wednesday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wednesday_follows_tuesday) ).
fof(f14,axiom,
consecutive(wednesday) = thursday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thursday_follows_wednesday) ).
fof(f15,axiom,
consecutive(thursday) = friday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',friday_follows_thursday) ).
fof(f16,axiom,
consecutive(friday) = saturday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',saturday_follows_friday) ).
fof(f17,axiom,
consecutive(saturday) = sunday,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sunday_follows_saturday) ).
fof(f18,axiom,
! [X0] :
( day1(X0)
<=> day2(consecutive(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day2_follows_day1) ).
fof(f19,axiom,
! [X0] :
( day2(X0)
<=> day3(consecutive(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',day3_follows_day2) ).
fof(f20,axiom,
! [X0] :
( day1(X0)
=> ( truthday(X0)
<=> ( ~ truthday(monday)
& ~ truthday(tuesday) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement1) ).
fof(f21,axiom,
! [X0] :
( day2(X0)
=> ( truthday(X0)
<=> ( day2(thursday)
| day2(saturday)
| day2(sunday) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement2) ).
fof(f22,axiom,
! [X0] :
( day3(X0)
=> ( truthday(X0)
<=> ( ~ truthday(wednesday)
& ~ truthday(friday) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',statement3) ).
fof(f23,conjecture,
truthday(tuesday),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tuesday_leo_tells_truths) ).
fof(f24,negated_conjecture,
~ truthday(tuesday),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,plain,
~ truthday(tuesday),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ~ truthday(X0)
| ~ truthday(X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( X0 = X1
| ~ truthday(X0)
| ~ truthday(X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( X0 = X1
| ~ day1(X0)
| ~ day1(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( X0 = X1
| ~ day1(X0)
| ~ day1(X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( X0 = X1
| ~ day2(X0)
| ~ day2(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f31,plain,
! [X0,X1] :
( X0 = X1
| ~ day2(X0)
| ~ day2(X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = X1
| ~ day3(X0)
| ~ day3(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f33,plain,
! [X0,X1] :
( X0 = X1
| ~ day3(X0)
| ~ day3(X1) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ( truthday(X0)
<=> ( ~ truthday(monday)
& ~ truthday(tuesday) ) )
| ~ day1(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0] :
( ( truthday(X0)
<=> ( day2(thursday)
| day2(saturday)
| day2(sunday) ) )
| ~ day2(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0] :
( ( truthday(X0)
<=> ( ~ truthday(wednesday)
& ~ truthday(friday) ) )
| ~ day3(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f37,plain,
truthday(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f7]) ).
fof(f38,plain,
day1(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f8]) ).
fof(f39,plain,
day2(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f9]) ).
fof(f40,plain,
day3(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f10]) ).
fof(f41,plain,
! [X0] :
( ( day1(X0)
| ~ day2(consecutive(X0)) )
& ( day2(consecutive(X0))
| ~ day1(X0) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f42,plain,
! [X0] :
( ( day2(X0)
| ~ day3(consecutive(X0)) )
& ( day3(consecutive(X0))
| ~ day2(X0) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] :
( ( ( truthday(X0)
| truthday(monday)
| truthday(tuesday) )
& ( ( ~ truthday(monday)
& ~ truthday(tuesday) )
| ~ truthday(X0) ) )
| ~ day1(X0) ),
inference(nnf_transformation,[],[f34]) ).
fof(f44,plain,
! [X0] :
( ( ( truthday(X0)
| truthday(monday)
| truthday(tuesday) )
& ( ( ~ truthday(monday)
& ~ truthday(tuesday) )
| ~ truthday(X0) ) )
| ~ day1(X0) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0] :
( ( ( truthday(X0)
| ( ~ day2(thursday)
& ~ day2(saturday)
& ~ day2(sunday) ) )
& ( day2(thursday)
| day2(saturday)
| day2(sunday)
| ~ truthday(X0) ) )
| ~ day2(X0) ),
inference(nnf_transformation,[],[f35]) ).
fof(f46,plain,
! [X0] :
( ( ( truthday(X0)
| ( ~ day2(thursday)
& ~ day2(saturday)
& ~ day2(sunday) ) )
& ( day2(thursday)
| day2(saturday)
| day2(sunday)
| ~ truthday(X0) ) )
| ~ day2(X0) ),
inference(flattening,[],[f45]) ).
fof(f47,plain,
! [X0] :
( ( ( truthday(X0)
| truthday(wednesday)
| truthday(friday) )
& ( ( ~ truthday(wednesday)
& ~ truthday(friday) )
| ~ truthday(X0) ) )
| ~ day3(X0) ),
inference(nnf_transformation,[],[f36]) ).
fof(f48,plain,
! [X0] :
( ( ( truthday(X0)
| truthday(wednesday)
| truthday(friday) )
& ( ( ~ truthday(wednesday)
& ~ truthday(friday) )
| ~ truthday(X0) ) )
| ~ day3(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( monday = X0
| tuesday = X0
| wednesday = X0
| thursday = X0
| friday = X0
| saturday = X0
| sunday = X0 ),
inference(cnf_transformation,[],[f1]) ).
fof(f50,plain,
saturday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f51,plain,
friday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f52,plain,
friday != saturday,
inference(cnf_transformation,[],[f2]) ).
fof(f53,plain,
thursday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f54,plain,
thursday != saturday,
inference(cnf_transformation,[],[f2]) ).
fof(f55,plain,
thursday != friday,
inference(cnf_transformation,[],[f2]) ).
fof(f56,plain,
wednesday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f57,plain,
wednesday != saturday,
inference(cnf_transformation,[],[f2]) ).
fof(f58,plain,
wednesday != friday,
inference(cnf_transformation,[],[f2]) ).
fof(f59,plain,
wednesday != thursday,
inference(cnf_transformation,[],[f2]) ).
fof(f60,plain,
tuesday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f61,plain,
tuesday != saturday,
inference(cnf_transformation,[],[f2]) ).
fof(f62,plain,
tuesday != friday,
inference(cnf_transformation,[],[f2]) ).
fof(f63,plain,
tuesday != thursday,
inference(cnf_transformation,[],[f2]) ).
fof(f64,plain,
tuesday != wednesday,
inference(cnf_transformation,[],[f2]) ).
fof(f65,plain,
monday != sunday,
inference(cnf_transformation,[],[f2]) ).
fof(f66,plain,
monday != saturday,
inference(cnf_transformation,[],[f2]) ).
fof(f67,plain,
monday != friday,
inference(cnf_transformation,[],[f2]) ).
fof(f68,plain,
monday != thursday,
inference(cnf_transformation,[],[f2]) ).
fof(f69,plain,
monday != wednesday,
inference(cnf_transformation,[],[f2]) ).
fof(f70,plain,
monday != tuesday,
inference(cnf_transformation,[],[f2]) ).
fof(f71,plain,
! [X0,X1] :
( X0 = X1
| ~ truthday(X0)
| ~ truthday(X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f72,plain,
! [X0,X1] :
( X0 = X1
| ~ day1(X0)
| ~ day1(X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| ~ day2(X0)
| ~ day2(X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ~ day3(X0)
| ~ day3(X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f75,plain,
truthday(sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f76,plain,
day1(sK1),
inference(cnf_transformation,[],[f38]) ).
fof(f77,plain,
day2(sK2),
inference(cnf_transformation,[],[f39]) ).
fof(f78,plain,
day3(sK3),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
monday = consecutive(sunday),
inference(cnf_transformation,[],[f11]) ).
fof(f80,plain,
tuesday = consecutive(monday),
inference(cnf_transformation,[],[f12]) ).
fof(f81,plain,
wednesday = consecutive(tuesday),
inference(cnf_transformation,[],[f13]) ).
fof(f82,plain,
thursday = consecutive(wednesday),
inference(cnf_transformation,[],[f14]) ).
fof(f83,plain,
friday = consecutive(thursday),
inference(cnf_transformation,[],[f15]) ).
fof(f84,plain,
saturday = consecutive(friday),
inference(cnf_transformation,[],[f16]) ).
fof(f85,plain,
sunday = consecutive(saturday),
inference(cnf_transformation,[],[f17]) ).
fof(f86,plain,
! [X0] :
( day2(consecutive(X0))
| ~ day1(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f87,plain,
! [X0] :
( day1(X0)
| ~ day2(consecutive(X0)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f88,plain,
! [X0] :
( day3(consecutive(X0))
| ~ day2(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f89,plain,
! [X0] :
( day2(X0)
| ~ day3(consecutive(X0)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f90,plain,
! [X0] :
( ~ truthday(tuesday)
| ~ truthday(X0)
| ~ day1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f91,plain,
! [X0] :
( ~ truthday(monday)
| ~ truthday(X0)
| ~ day1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f92,plain,
! [X0] :
( truthday(X0)
| truthday(monday)
| truthday(tuesday)
| ~ day1(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f93,plain,
! [X0] :
( day2(thursday)
| day2(saturday)
| day2(sunday)
| ~ truthday(X0)
| ~ day2(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f94,plain,
! [X0] :
( truthday(X0)
| ~ day2(sunday)
| ~ day2(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0] :
( truthday(X0)
| ~ day2(saturday)
| ~ day2(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f96,plain,
! [X0] :
( truthday(X0)
| ~ day2(thursday)
| ~ day2(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f97,plain,
! [X0] :
( ~ truthday(friday)
| ~ truthday(X0)
| ~ day3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f98,plain,
! [X0] :
( ~ truthday(wednesday)
| ~ truthday(X0)
| ~ day3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f99,plain,
! [X0] :
( truthday(X0)
| truthday(wednesday)
| truthday(friday)
| ~ day3(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f100,plain,
~ truthday(tuesday),
inference(cnf_transformation,[],[f25]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| day1(X0)
| day1(X1) ),
inference(consistent_polarity_flipping,[],[f72]) ).
fof(f102,plain,
~ day1(sK1),
inference(consistent_polarity_flipping,[],[f76]) ).
fof(f103,plain,
! [X0] :
( ~ day1(X0)
| ~ day2(consecutive(X0)) ),
inference(consistent_polarity_flipping,[],[f87]) ).
fof(f104,plain,
! [X0] :
( day2(consecutive(X0))
| day1(X0) ),
inference(consistent_polarity_flipping,[],[f86]) ).
fof(f105,plain,
! [X0] :
( truthday(X0)
| truthday(monday)
| truthday(tuesday)
| day1(X0) ),
inference(consistent_polarity_flipping,[],[f92]) ).
fof(f106,plain,
! [X0] :
( ~ truthday(monday)
| ~ truthday(X0)
| day1(X0) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f107,plain,
! [X0] :
( ~ truthday(tuesday)
| ~ truthday(X0)
| day1(X0) ),
inference(consistent_polarity_flipping,[],[f90]) ).
fof(f218,plain,
$false,
inference(finite_model_not_found_(exhaustively_excluded_all_possible_domain_size_assignments),[],[f49,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f71,f101,f73,f74,f75,f102,f77,f78,f79,f80,f81,f82,f83,f84,f85,f103,f104,f89,f88,f105,f106,f107,f96,f95,f94,f93,f99,f98,f97,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ078+1 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:40:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 Running first-order model finding
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % (243197)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (243207)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2373605075:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (243203)% WARNING: option uhcvi not known.
% 0.11/0.45 % (243202)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3099246521_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.45 % (243204)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=739096848:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.45 % (243205)dis+10_1_sil=32000:sp=arity:random_seed=1328865636:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.45 % (243206)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3156471096:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (243208)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4265972026:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.45 % (243203)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=606933623:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.45 % Detected minimum model sizes of [7]
% 0.11/0.45 % Detected maximum model sizes of [7]
% 0.11/0.45 % TRYING [7]
% 0.11/0.45 % (243202) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-243197-243202"...
% 0.11/0.45 % (243202)...printing done.
% 0.11/0.45 % (243202)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (243202)------------------------------
% 0.11/0.45 % (243202)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (243202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (243202)CaDiCaL version: 2.1.3
% 0.11/0.45 % (243202)Termination reason: Refutation
% 0.11/0.45 % (243202)Time elapsed: 0.006 s
% 0.11/0.45 % (243202)Peak memory usage: 12 MB
% 0.11/0.45 % (243202)Instructions burned: 11 (million)
% 0.11/0.45 % (243197)Success in time 0.033 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------