%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX079_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 : n013.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 01:46:27 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 148 ( 51 ~; 42 |; 49 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 103 ( 45 atm; 0 fun; 22 num; 36 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 : 15 ( 9 usr; 2 prp; 0-2 aty)
% Number of functors : 18 ( 17 usr; 5 con; 0-1 aty)
% Number of variables : 52 ( 30 !; 22 ?; 52 :)
% 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 > $int ).
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 > $int ).
tff(func_def_18,type,
sK9: general > $int ).
tff(func_def_19,type,
sK10: general > $int ).
tff(func_def_20,type,
sK11: general ).
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,
s: ( general * general ) > $o ).
tff(pred_def_9,type,
covered: general > $o ).
tff(pred_def_10,type,
in_cover: 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(f22,conjecture,
! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( ( X0 = f__integer__(X1) )
& $greatereq(X1,1)
& $lesseq(X1,n_i) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_6_unnamed_formula) ).
tff(f23,negated_conjecture,
~ ! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( ( X0 = f__integer__(X1) )
& $greatereq(X1,1)
& $lesseq(X1,n_i) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
tff(f27,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(f28,plain,
~ ! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( ( X0 = f__integer__(X1) )
& ~ $less(X1,1)
& ~ $less(n_i,X1) ) ),
inference(theory_normalization,[],[f23]) ).
tff(f46,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,[],[f27]) ).
tff(f62,plain,
? [X0: general] :
( ! [X1: $int] :
( ( f__integer__(X1) != X0 )
| $less(X1,1)
| $less(n_i,X1) )
& in_cover(X0) ),
inference(ennf_transformation,[],[f28]) ).
tff(f71,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,[],[f46]) ).
tff(f72,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,[],[f71]) ).
tff(f73,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,[],[f72]) ).
tff(f74,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 = sK8(X0) )
& ( n_i = sK9(X0) )
& ( f__integer__(sK10(X0)) = X0 )
& ~ $less(sK10(X0),sK8(X0))
& ~ $less(sK9(X0),sK10(X0))
& in_cover(X0) )
| ~ in_cover(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X4,sK8(X0)),skolemize(X5,sK9(X0)),skolemize(X6,sK10(X0))],[f73]) ).
tff(f75,plain,
( ! [X1: $int] :
( ( f__integer__(X1) != sK11 )
| $less(X1,1)
| $less(n_i,X1) )
& in_cover(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X0,sK11)],[f62]) ).
tff(f106,plain,
! [X0: general] :
( ~ in_cover(X0)
| ~ $less(sK9(X0),sK10(X0)) ),
inference(cnf_transformation,[],[f74]) ).
tff(f107,plain,
! [X0: general] :
( ~ in_cover(X0)
| ~ $less(sK10(X0),sK8(X0)) ),
inference(cnf_transformation,[],[f74]) ).
tff(f108,plain,
! [X0: general] :
( ~ in_cover(X0)
| ( f__integer__(sK10(X0)) = X0 ) ),
inference(cnf_transformation,[],[f74]) ).
tff(f109,plain,
! [X0: general] :
( ~ in_cover(X0)
| ( n_i = sK9(X0) ) ),
inference(cnf_transformation,[],[f74]) ).
tff(f110,plain,
! [X0: general] :
( ~ in_cover(X0)
| ( 1 = sK8(X0) ) ),
inference(cnf_transformation,[],[f74]) ).
tff(f112,plain,
in_cover(sK11),
inference(cnf_transformation,[],[f75]) ).
tff(f113,plain,
! [X1: $int] :
( ( f__integer__(X1) != sK11 )
| $less(X1,1)
| $less(n_i,X1) ),
inference(cnf_transformation,[],[f75]) ).
tff(f123,plain,
n_i = sK9(sK11),
inference(resolution,[],[f109,f112]) ).
tff(f124,plain,
1 = sK8(sK11),
inference(resolution,[],[f110,f112]) ).
tff(f129,plain,
~ $less(sK9(sK11),sK10(sK11)),
inference(resolution,[],[f106,f112]) ).
tff(f130,plain,
~ $less(n_i,sK10(sK11)),
inference(forward_demodulation,[],[f129,f123]) ).
tff(f131,plain,
~ $less(sK10(sK11),sK8(sK11)),
inference(resolution,[],[f107,f112]) ).
tff(f132,plain,
~ $less(sK10(sK11),1),
inference(forward_demodulation,[],[f131,f124]) ).
tff(f133,plain,
sK11 = f__integer__(sK10(sK11)),
inference(resolution,[],[f108,f112]) ).
tff(f136,plain,
( ( sK11 != sK11 )
| $less(sK10(sK11),1)
| $less(n_i,sK10(sK11)) ),
inference(superposition,[],[f113,f133]) ).
tff(f141,plain,
( $less(sK10(sK11),1)
| $less(n_i,sK10(sK11)) ),
inference(trivial_inequality_removal,[],[f136]) ).
tff(f142,plain,
$less(n_i,sK10(sK11)),
inference(forward_subsumption_resolution,[],[f141,f132]) ).
tff(f143,plain,
$false,
inference(forward_subsumption_resolution,[],[f142,f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX079_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n013.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 14:59:21 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.23 Running first-order model finding
% 0.07/0.23 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
% 0.20/0.28 % (1245069)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1245074)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2445104115_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (1245074)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.28 % (1245074)Terminated due to inappropriate strategy.
% 0.20/0.28 % (1245074)------------------------------
% 0.20/0.28 % (1245074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1245074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1245074)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1245074)Termination reason: Inappropriate
% 0.20/0.28 % (1245074)Time elapsed: 0.001 s
% 0.20/0.28 % (1245074)Peak memory usage: 11 MB
% 0.20/0.28 % (1245074)Instructions burned: 2 (million)
% 0.20/0.28 % (1245074)------------------------------
% 0.20/0.28 % (1245074)------------------------------
% 0.20/0.28 % (1245075)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1245076)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4154993549:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1245075)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3907570469:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1245079)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=982494358:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1245077)dis+10_1_sil=32000:sp=arity:random_seed=1087361618:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1245078)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=496875155:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1245080)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2334192567:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (1245079) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1245069-1245079"...
% 0.20/0.28 % (1245077) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1245069-1245077"...
% 0.20/0.28 % (1245075) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1245069-1245075"...
% 0.20/0.28 % (1245078) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1245069-1245078"...
% 0.20/0.28 % (1245080) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1245069-1245080"...
% 0.20/0.28 % (1245082)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1378552032:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % (1245079)...printing done.
% 0.20/0.28 % (1245075)...printing done.
% 0.20/0.28 % (1245077)...printing done.
% 0.20/0.28 % (1245078)...printing done.
% 0.20/0.28 % (1245082)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.28 % (1245082)Terminated due to inappropriate strategy.
% 0.20/0.28 % (1245082)------------------------------
% 0.20/0.28 % (1245082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1245082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1245082)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1245082)Termination reason: Inappropriate
% 0.20/0.28 % (1245082)Time elapsed: 0.0000 s
% 0.20/0.28 % (1245082)Peak memory usage: 11 MB
% 0.20/0.28 % (1245082)Instructions burned: 1 (million)
% 0.20/0.28 % (1245079)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1245079)------------------------------
% 0.20/0.28 % (1245079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1245079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1245079)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1245079)Termination reason: Refutation
% 0.20/0.28 % (1245079)Time elapsed: 0.004 s
% 0.20/0.28 % (1245079)Peak memory usage: 12 MB
% 0.20/0.28 % (1245079)Instructions burned: 5 (million)
% 0.20/0.28 % (1245069)Success in time 0.038 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------