%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX078_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 01:46:26 PM UTC 2026
% Result : Theorem 0.12s 0.24s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 276 ( 92 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 329 ( 116 ~; 108 |; 93 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 190 ( 76 atm; 0 fun; 38 num; 76 var)
% Number of types : 4 ( 2 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 14 usr; 6 prp; 0-2 aty)
% Number of functors : 25 ( 24 usr; 8 con; 0-1 aty)
% Number of variables : 101 ( 0 sgn 55 !; 46 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
general: $tType ).
tff(type_def_6,type,
symbol: $tType ).
tff(func_def_0,type,
f__integer__: $int > general ).
tff(func_def_1,type,
f__symbolic__: symbol > general ).
tff(func_def_2,type,
c__infimum__: general ).
tff(func_def_3,type,
c__supremum__: general ).
tff(func_def_4,type,
n_i: $int ).
tff(func_def_9,type,
sK0: general > $int ).
tff(func_def_10,type,
sK1: general > symbol ).
tff(func_def_11,type,
sK2: general > general ).
tff(func_def_12,type,
sK3: general > general ).
tff(func_def_13,type,
sK4: general > general ).
tff(func_def_14,type,
sK5: general > general ).
tff(func_def_15,type,
sK6: general > general ).
tff(func_def_16,type,
sK7: general > general ).
tff(func_def_17,type,
sK8: general > general ).
tff(func_def_18,type,
sK9: general > general ).
tff(func_def_19,type,
sK10: general > general ).
tff(func_def_20,type,
sK11: general > general ).
tff(func_def_21,type,
sK12: general > $int ).
tff(func_def_22,type,
sK13: general > $int ).
tff(func_def_23,type,
sK14: general > $int ).
tff(func_def_24,type,
sK15: general ).
tff(func_def_25,type,
sK16: $int ).
tff(func_def_26,type,
sK17: $int ).
tff(func_def_27,type,
sK18: $int ).
tff(pred_def_1,type,
p__is_integer__: general > $o ).
tff(pred_def_2,type,
p__is_symbolic__: general > $o ).
tff(pred_def_3,type,
p__less_equal__: ( general * general ) > $o ).
tff(pred_def_4,type,
p__less__: ( general * general ) > $o ).
tff(pred_def_5,type,
p__greater_equal__: ( general * general ) > $o ).
tff(pred_def_6,type,
p__greater__: ( general * general ) > $o ).
tff(pred_def_8,type,
covered: general > $o ).
tff(pred_def_9,type,
in_cover: general > $o ).
tff(pred_def_10,type,
s: ( general * general ) > $o ).
tff(pred_def_11,type,
covered_p: general > $o ).
tff(f21,axiom,
! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& $lesseq(X1,X3)
& $lesseq(X3,X2) )
& $true
& in_cover(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_5_completed_definition_of_in_cover_1) ).
tff(f24,conjecture,
! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& $lesseq(X1,X3)
& $lesseq(X3,X2) )
& $true
& in_cover(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_8_completed_definition_of_in_cover_1) ).
tff(f25,negated_conjecture,
~ ! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& $lesseq(X1,X3)
& $lesseq(X3,X2) )
& $true
& in_cover(X0) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
tff(f28,plain,
! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& $true
& in_cover(X0) ) ),
inference(theory_normalization,[],[f21]) ).
tff(f29,plain,
~ ! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& $true
& in_cover(X0) ) ),
inference(theory_normalization,[],[f25]) ).
tff(f48,plain,
! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) ) ),
inference(true_and_false_elimination,[],[f28]) ).
tff(f53,plain,
~ ! [X0: general] :
( in_cover(X0)
<=> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) ) ),
inference(true_and_false_elimination,[],[f29]) ).
tff(f70,plain,
? [X0: general] :
( in_cover(X0)
<~> ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) ) ),
inference(ennf_transformation,[],[f53]) ).
tff(f80,plain,
! [X0: general] :
( ( in_cover(X0)
| ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0) )
& ( ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) )
| ~ in_cover(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
tff(f81,plain,
! [X0: general] :
( ( in_cover(X0)
| ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0) )
& ( ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) )
| ~ in_cover(X0) ) ),
inference(flattening,[],[f80]) ).
tff(f82,plain,
! [X0: general] :
( ( in_cover(X0)
| ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0) )
& ( ( ? [X4: $int,X5: $int,X6: $int] :
( ( 1 = X4 )
& ( n_i = X5 )
& ( f__integer__(X6) = X0 )
& ~ $less(X6,X4)
& ~ $less(X5,X6) )
& in_cover(X0) )
| ~ in_cover(X0) ) ),
inference(rectify,[],[f81]) ).
tff(f83,plain,
! [X0: general] :
( ( in_cover(X0)
| ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0) )
& ( ( ( 1 = sK12(X0) )
& ( n_i = sK13(X0) )
& ( f__integer__(sK14(X0)) = X0 )
& ~ $less(sK14(X0),sK12(X0))
& ~ $less(sK13(X0),sK14(X0))
& in_cover(X0) )
| ~ in_cover(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X4,sK12(X0)),skolemize(X5,sK13(X0)),skolemize(X6,sK14(X0))],[f82]) ).
tff(f84,plain,
? [X0: general] :
( ( ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0)
| ~ in_cover(X0) )
& ( ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) )
| in_cover(X0) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f85,plain,
? [X0: general] :
( ( ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0)
| ~ in_cover(X0) )
& ( ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X3,X1)
& ~ $less(X2,X3) )
& in_cover(X0) )
| in_cover(X0) ) ),
inference(flattening,[],[f84]) ).
tff(f86,plain,
? [X0: general] :
( ( ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(X0)
| ~ in_cover(X0) )
& ( ( ? [X4: $int,X5: $int,X6: $int] :
( ( 1 = X4 )
& ( n_i = X5 )
& ( f__integer__(X6) = X0 )
& ~ $less(X6,X4)
& ~ $less(X5,X6) )
& in_cover(X0) )
| in_cover(X0) ) ),
inference(rectify,[],[f85]) ).
tff(f87,plain,
( ( ! [X1: $int,X2: $int,X3: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != sK15 )
| $less(X3,X1)
| $less(X2,X3) )
| ~ in_cover(sK15)
| ~ in_cover(sK15) )
& ( ( ( 1 = sK16 )
& ( n_i = sK17 )
& ( sK15 = f__integer__(sK18) )
& ~ $less(sK18,sK16)
& ~ $less(sK17,sK18)
& in_cover(sK15) )
| in_cover(sK15) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17,sK18]),skolemize(X0,sK15),skolemize(X4,sK16),skolemize(X5,sK17),skolemize(X6,sK18)],[f86]) ).
tff(f122,plain,
! [X0: general] :
( ~ $less(sK13(X0),sK14(X0))
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f123,plain,
! [X0: general] :
( ~ $less(sK14(X0),sK12(X0))
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f124,plain,
! [X0: general] :
( ( f__integer__(sK14(X0)) = X0 )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f125,plain,
! [X0: general] :
( ( n_i = sK13(X0) )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f126,plain,
! [X0: general] :
( ( 1 = sK12(X0) )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f83]) ).
tff(f130,plain,
( in_cover(sK15)
| in_cover(sK15) ),
inference(cnf_transformation,[],[f87]) ).
tff(f136,plain,
! [X2: $int,X3: $int,X1: $int] :
( ( 1 != X1 )
| ( n_i != X2 )
| ( f__integer__(X3) != sK15 )
| $less(X3,X1)
| $less(X2,X3)
| ~ in_cover(sK15)
| ~ in_cover(sK15) ),
inference(cnf_transformation,[],[f87]) ).
tff(f165,plain,
! [X2: $int,X3: $int] :
( ( n_i != X2 )
| ( f__integer__(X3) != sK15 )
| $less(X3,1)
| $less(X2,X3)
| ~ in_cover(sK15)
| ~ in_cover(sK15) ),
inference(equality_resolution,[],[f136]) ).
tff(f166,plain,
! [X3: $int] :
( ( f__integer__(X3) != sK15 )
| $less(X3,1)
| $less(n_i,X3)
| ~ in_cover(sK15)
| ~ in_cover(sK15) ),
inference(equality_resolution,[],[f165]) ).
tff(f187,plain,
! [X0: general] :
( in_cover(X0)
| ( 1 = sK12(X0) ) ),
inference(consistent_polarity_flipping,[],[f126]) ).
tff(f188,plain,
! [X0: general] :
( in_cover(X0)
| ( n_i = sK13(X0) ) ),
inference(consistent_polarity_flipping,[],[f125]) ).
tff(f189,plain,
! [X0: general] :
( in_cover(X0)
| ( f__integer__(sK14(X0)) = X0 ) ),
inference(consistent_polarity_flipping,[],[f124]) ).
tff(f190,plain,
! [X0: general] :
( in_cover(X0)
| ~ $less(sK14(X0),sK12(X0)) ),
inference(consistent_polarity_flipping,[],[f123]) ).
tff(f191,plain,
! [X0: general] :
( in_cover(X0)
| ~ $less(sK13(X0),sK14(X0)) ),
inference(consistent_polarity_flipping,[],[f122]) ).
tff(f195,plain,
! [X3: $int] :
( ( f__integer__(X3) != sK15 )
| $less(X3,1)
| $less(n_i,X3)
| in_cover(sK15)
| in_cover(sK15) ),
inference(consistent_polarity_flipping,[],[f166]) ).
tff(f201,plain,
( ~ in_cover(sK15)
| ~ in_cover(sK15) ),
inference(consistent_polarity_flipping,[],[f130]) ).
tff(f202,plain,
~ in_cover(sK15),
inference(duplicate_literal_removal,[],[f201]) ).
tff(f203,plain,
! [X3: $int] :
( ( f__integer__(X3) != sK15 )
| $less(X3,1)
| $less(n_i,X3)
| in_cover(sK15) ),
inference(duplicate_literal_removal,[],[f195]) ).
tff(f205,definition,
( spl19_1
<=> in_cover(sK15) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
tff(f207,plain,
( in_cover(sK15)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f205]) ).
tff(f209,definition,
( spl19_2
<=> ! [X3: $int] :
( ( f__integer__(X3) != sK15 )
| $less(n_i,X3)
| $less(X3,1) ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
tff(f210,plain,
( ! [X3: $int] :
( ( f__integer__(X3) != sK15 )
| $less(n_i,X3)
| $less(X3,1) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f209]) ).
tff(f211,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f203,f209,f205]) ).
tff(f220,plain,
1 = sK12(sK15),
inference(resolution,[],[f187,f202]) ).
tff(f222,plain,
n_i = sK13(sK15),
inference(resolution,[],[f188,f202]) ).
tff(f246,plain,
sK15 = f__integer__(sK14(sK15)),
inference(resolution,[],[f189,f202]) ).
tff(f253,plain,
( ( sK15 != sK15 )
| $less(n_i,sK14(sK15))
| $less(sK14(sK15),1)
| ~ spl19_2 ),
inference(superposition,[],[f210,f246]) ).
tff(f254,plain,
( $less(n_i,sK14(sK15))
| $less(sK14(sK15),1)
| ~ spl19_2 ),
inference(trivial_inequality_removal,[],[f253]) ).
tff(f256,definition,
( spl19_3
<=> $less(sK14(sK15),1) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
tff(f260,definition,
( spl19_4
<=> $less(n_i,sK14(sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
tff(f263,plain,
( spl19_3
| spl19_4
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f254,f209,f260,f256]) ).
tff(f266,plain,
~ $less(sK14(sK15),sK12(sK15)),
inference(resolution,[],[f190,f202]) ).
tff(f269,plain,
~ $less(sK14(sK15),1),
inference(superposition,[],[f266,f220]) ).
tff(f270,plain,
~ spl19_3,
inference(avatar_split_clause,[],[f269,f256]) ).
tff(f271,plain,
~ $less(sK13(sK15),sK14(sK15)),
inference(resolution,[],[f191,f202]) ).
tff(f274,plain,
~ $less(n_i,sK14(sK15)),
inference(superposition,[],[f271,f222]) ).
tff(f275,plain,
~ spl19_4,
inference(avatar_split_clause,[],[f274,f260]) ).
tff(f276,plain,
( $false
| ~ spl19_1 ),
inference(resolution,[],[f207,f202]) ).
tff(f277,plain,
~ spl19_1,
inference(avatar_contradiction_clause,[],[f276]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f211]) ).
cnf(s2,plain,
( ~ spl19_2
| spl19_3
| spl19_4 ),
inference(sat_conversion,[],[f263]) ).
cnf(s3,plain,
~ spl19_3,
inference(sat_conversion,[],[f270]) ).
cnf(s4,plain,
~ spl19_4,
inference(sat_conversion,[],[f275]) ).
cnf(s5,plain,
~ spl19_1,
inference(sat_conversion,[],[f277]) ).
cnf(s6,plain,
~ spl19_2,
inference(rat,[],[s2,s4,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s5]) ).
tff(f278,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX078_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.16 % Computer : n002.cluster.edu
% 0.12/0.16 % Model : x86_64 x86_64
% 0.12/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.16 % Memory : 8046.5625MB
% 0.12/0.16 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Mon Sep 28 15:02:37 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.20 Running first-order model finding
% 0.12/0.20 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
% 0.12/0.24 % (418336)Will run a generic schedule for satisfiability detection.
% 0.12/0.24 % (418357)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3906393383:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.24 % (418357) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-418336-418357"...
% 0.12/0.24 % (418351)% WARNING: option uhcvi not known.
% 0.12/0.24 % (418357)...printing done.
% 0.12/0.24 % (418357)Refutation found. Thanks to Tanya!
% 0.12/0.24 % SZS status Theorem for theBenchmark
% 0.12/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.25 % (418357)------------------------------
% 0.12/0.25 % (418357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.25 % (418357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.25 % (418357)CaDiCaL version: 2.1.3
% 0.12/0.25 % (418357)Termination reason: Refutation
% 0.12/0.25 % (418357)Time elapsed: 0.004 s
% 0.12/0.25 % (418357)Peak memory usage: 12 MB
% 0.12/0.25 % (418357)Instructions burned: 8 (million)
% 0.12/0.25 % (418336)Success in time 0.035 s
% 0.12/0.25 % Vampire exiting
%------------------------------------------------------------------------------