%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX079_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 01:45:50 PM UTC 2026
% Result : Theorem 5.67s 1.96s
% Output : Refutation 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 146 ( 46 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 181 ( 69 ~; 56 |; 49 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 101 ( 44 atm; 0 fun; 21 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 : 16 ( 10 usr; 3 prp; 0-2 aty)
% Number of functors : 18 ( 17 usr; 5 con; 0-1 aty)
% Number of variables : 60 ( 38 !; 22 ?; 60 :)
% 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_7,type,
sK0: general > general ).
tff(func_def_8,type,
sK1: general > general ).
tff(func_def_9,type,
sK2: general > general ).
tff(func_def_10,type,
sK3: general > general ).
tff(func_def_11,type,
sK4: general > general ).
tff(func_def_12,type,
sK5: general ).
tff(func_def_13,type,
sK6: general > $int ).
tff(func_def_14,type,
sK7: general > $int ).
tff(func_def_15,type,
sK8: general > $int ).
tff(func_def_16,type,
sK9: general > symbol ).
tff(func_def_17,type,
sK10: general > $int ).
tff(func_def_18,type,
sK11: general > $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,
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] :
( ( ? [X1: $int,X2: $int,X3: $int] :
( ( X1 = 1 )
& $lesseq(X1,X3)
& ( X0 = f__integer__(X3) )
& ( X2 = n_i )
& $lesseq(X3,X2) )
& $true
& in_cover(X0) )
<=> in_cover(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_5_completed_definition_of_in_cover_1) ).
tff(f22,conjecture,
! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( $lesseq(X1,n_i)
& $greatereq(X1,1)
& ( X0 = f__integer__(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_6_unnamed_formula) ).
tff(f23,negated_conjecture,
~ ! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( $lesseq(X1,n_i)
& $greatereq(X1,1)
& ( X0 = f__integer__(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
tff(f24,plain,
! [X0: general] :
( ( ? [X2: $int,X3: $int,X1: $int] :
( ~ $less(X3,X1)
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X2,X3)
& ( X1 = 1 ) )
& $true
& in_cover(X0) )
<=> in_cover(X0) ),
inference(theory_normalization,[],[f21]) ).
tff(f28,plain,
~ ! [X0: general] :
( in_cover(X0)
=> ? [X1: $int] :
( ~ $less(n_i,X1)
& ~ $less(X1,1)
& ( X0 = f__integer__(X1) ) ) ),
inference(theory_normalization,[],[f23]) ).
tff(f30,plain,
! [X0: general] :
( ( ? [X2: $int,X3: $int,X1: $int] :
( ~ $less(X3,X1)
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X2,X3)
& ( X1 = 1 ) )
& in_cover(X0) )
<=> in_cover(X0) ),
inference(true_and_false_elimination,[],[f24]) ).
tff(f43,plain,
? [X0: general] :
( ! [X1: $int] :
( $less(n_i,X1)
| $less(X1,1)
| ( f__integer__(X1) != X0 ) )
& in_cover(X0) ),
inference(ennf_transformation,[],[f28]) ).
tff(f60,plain,
( ! [X1: $int] :
( $less(n_i,X1)
| $less(X1,1)
| ( f__integer__(X1) != sK5 ) )
& in_cover(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f43]) ).
tff(f63,plain,
! [X0: general] :
( ( ( ? [X2: $int,X3: $int,X1: $int] :
( ~ $less(X3,X1)
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X2,X3)
& ( X1 = 1 ) )
& in_cover(X0) )
| ~ in_cover(X0) )
& ( in_cover(X0)
| ! [X2: $int,X3: $int,X1: $int] :
( $less(X3,X1)
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X2,X3)
| ( 1 != X1 ) )
| ~ in_cover(X0) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f64,plain,
! [X0: general] :
( ( ( ? [X2: $int,X3: $int,X1: $int] :
( ~ $less(X3,X1)
& ( X2 = n_i )
& ( X0 = f__integer__(X3) )
& ~ $less(X2,X3)
& ( X1 = 1 ) )
& in_cover(X0) )
| ~ in_cover(X0) )
& ( in_cover(X0)
| ! [X2: $int,X3: $int,X1: $int] :
( $less(X3,X1)
| ( n_i != X2 )
| ( f__integer__(X3) != X0 )
| $less(X2,X3)
| ( 1 != X1 ) )
| ~ in_cover(X0) ) ),
inference(flattening,[],[f63]) ).
tff(f65,plain,
! [X0: general] :
( ( ( ? [X1: $int,X2: $int,X3: $int] :
( ~ $less(X2,X3)
& ( n_i = X1 )
& ( f__integer__(X2) = X0 )
& ~ $less(X1,X2)
& ( 1 = X3 ) )
& in_cover(X0) )
| ~ in_cover(X0) )
& ( in_cover(X0)
| ! [X4: $int,X5: $int,X6: $int] :
( $less(X5,X6)
| ( n_i != X4 )
| ( f__integer__(X5) != X0 )
| $less(X4,X5)
| ( 1 != X6 ) )
| ~ in_cover(X0) ) ),
inference(rectify,[],[f64]) ).
tff(f66,plain,
! [X0: general] :
( ( ( ~ $less(sK7(X0),sK8(X0))
& ( n_i = sK6(X0) )
& ( f__integer__(sK7(X0)) = X0 )
& ~ $less(sK6(X0),sK7(X0))
& ( 1 = sK8(X0) )
& in_cover(X0) )
| ~ in_cover(X0) )
& ( in_cover(X0)
| ! [X4: $int,X5: $int,X6: $int] :
( $less(X5,X6)
| ( n_i != X4 )
| ( f__integer__(X5) != X0 )
| $less(X4,X5)
| ( 1 != X6 ) )
| ~ in_cover(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X3,sK8(X0))],[f65]) ).
tff(f90,plain,
in_cover(sK5),
inference(cnf_transformation,[],[f60]) ).
tff(f91,plain,
! [X1: $int] :
( ( f__integer__(X1) != sK5 )
| $less(n_i,X1)
| $less(X1,1) ),
inference(cnf_transformation,[],[f60]) ).
tff(f96,plain,
! [X0: general] :
( ( 1 = sK8(X0) )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f97,plain,
! [X0: general] :
( ~ $less(sK6(X0),sK7(X0))
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f98,plain,
! [X0: general] :
( ( f__integer__(sK7(X0)) = X0 )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f99,plain,
! [X0: general] :
( ( n_i = sK6(X0) )
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f100,plain,
! [X0: general] :
( ~ $less(sK7(X0),sK8(X0))
| ~ in_cover(X0) ),
inference(cnf_transformation,[],[f66]) ).
tff(f130,definition,
( spl12_1
<=> in_cover(sK5) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
tff(f132,plain,
( in_cover(sK5)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f130]) ).
tff(f133,plain,
spl12_1,
inference(avatar_split_clause,[],[f90,f130]) ).
tff(f156,plain,
! [X0: general] :
( ~ $less(n_i,sK7(X0))
| ~ in_cover(X0)
| ~ in_cover(X0) ),
inference(superposition,[],[f97,f99]) ).
tff(f157,plain,
! [X0: general] :
( ~ $less(n_i,sK7(X0))
| ~ in_cover(X0) ),
inference(duplicate_literal_removal,[],[f156]) ).
tff(f166,plain,
! [X0: general] :
( $less(sK7(X0),1)
| $less(n_i,sK7(X0))
| ( sK5 != X0 )
| ~ in_cover(X0) ),
inference(superposition,[],[f91,f98]) ).
tff(f167,plain,
! [X0: general] :
( ~ $less(sK7(X0),1)
| ~ in_cover(X0)
| ~ in_cover(X0) ),
inference(superposition,[],[f100,f96]) ).
tff(f168,plain,
! [X0: general] :
( ~ $less(sK7(X0),1)
| ~ in_cover(X0) ),
inference(duplicate_literal_removal,[],[f167]) ).
tff(f266,plain,
! [X0: general] :
( ( sK5 != X0 )
| ~ in_cover(X0)
| $less(n_i,sK7(X0))
| ~ in_cover(X0) ),
inference(resolution,[],[f168,f166]) ).
tff(f267,plain,
! [X0: general] :
( $less(n_i,sK7(X0))
| ( sK5 != X0 )
| ~ in_cover(X0) ),
inference(duplicate_literal_removal,[],[f266]) ).
tff(f268,plain,
! [X0: general] :
( ( sK5 != X0 )
| ~ in_cover(X0) ),
inference(forward_subsumption_resolution,[],[f267,f157]) ).
tff(f269,plain,
~ in_cover(sK5),
inference(equality_resolution,[],[f268]) ).
tff(f270,plain,
( $false
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f269,f132]) ).
tff(f271,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f270]) ).
tff(f272,plain,
$false,
inference(avatar_smt_refutation,[],[f271,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWX079_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n019.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Mon Sep 28 15:00:03 UTC 2026
% 0.11/0.28 % CPUTime :
% 0.11/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.33 Running first-order theorem proving
% 0.26/0.33 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
% 3.80/1.62 % (4064364)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.80/1.62 % (4064371)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=543196561:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.80/1.62 % (4064372)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1045699279:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.80/1.62 % (4064371)Instruction limit reached!
% 3.80/1.62 % (4064371)------------------------------
% 3.80/1.62 % (4064371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.62 % (4064371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.62 % (4064371)CaDiCaL version: 2.1.3
% 3.80/1.62 % (4064371)Termination reason: Instruction limit
% 3.80/1.62 % (4064371)Termination phase: Saturation
% 3.80/1.62 % (4064371)Time elapsed: 0.028 s
% 3.80/1.62 % (4064371)Peak memory usage: 116 MB
% 3.80/1.62 % (4064371)Instructions burned: 13 (million)
% 3.80/1.62 % (4064372)First to succeed.
% 3.80/1.62 % (4064372)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4064364"
% 3.80/1.62 % (4064376)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=558714265:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.80/1.62 % (4064373)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4095658886:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.80/1.62 % (4064375)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4008006732:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.80/1.62 % (4064374)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3436318991:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.80/1.62 % (4064375)Instruction limit reached!
% 3.80/1.62 % (4064375)------------------------------
% 3.80/1.62 % (4064375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.62 % (4064375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.62 % (4064375)CaDiCaL version: 2.1.3
% 3.80/1.62 % (4064375)Termination reason: Instruction limit
% 3.80/1.62 % (4064375)Termination phase: Saturation
% 3.80/1.62 % (4064375)Time elapsed: 0.006 s
% 3.80/1.62 % (4064375)Peak memory usage: 88 MB
% 3.80/1.62 % (4064377)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2216353821:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.80/1.62 % (4064375)Instructions burned: 4 (million)
% 3.80/1.62 % (4064374)Instruction limit reached!
% 3.80/1.62 % (4064374)------------------------------
% 3.80/1.62 % (4064374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.62 % (4064374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.62 % (4064374)CaDiCaL version: 2.1.3
% 3.80/1.62 % (4064374)Termination reason: Instruction limit
% 3.80/1.62 % (4064374)Termination phase: Saturation
% 3.80/1.62 % (4064374)Time elapsed: 0.010 s
% 3.80/1.62 % (4064374)Peak memory usage: 88 MB
% 3.80/1.62 % (4064374)Instructions burned: 8 (million)
% 3.80/1.62 % (4064376)Also succeeded, but the first one will report.
% 3.80/1.62 % (4064377)Also succeeded, but the first one will report.
% 3.80/1.62 % (4064380)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1755333555:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.80/1.62 % (4064380)Also succeeded, but the first one will report.
% 3.80/1.62 % (4064373)Also succeeded, but the first one will report.
% 3.80/1.62 % (4064386)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1111412345:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.80/1.62 % (4064386)Also succeeded, but the first one will report.
% 3.80/1.62 % (4064387)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=232157102:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.80/1.62 % (4064387)Instruction limit reached!
% 3.80/1.62 % (4064387)------------------------------
% 3.80/1.62 % (4064387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.62 % (4064387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.96 % (4064387)CaDiCaL version: 2.1.3
% 5.67/1.96 % (4064387)Termination reason: Instruction limit
% 5.67/1.96 % (4064387)Termination phase: Saturation
% 5.67/1.96 % (4064387)Time elapsed: 0.020 s
% 5.67/1.96 % (4064387)Peak memory usage: 90 MB
% 5.67/1.96 % (4064387)Instructions burned: 16 (million)
% 5.67/1.96 % (4064372)Refutation found. Thanks to Tanya!
% 5.67/1.96 % SZS status Theorem for theBenchmark
% 5.67/1.96 % SZS output start Proof for theBenchmark
% See solution above
% 5.67/1.96 % (4064372)------------------------------
% 5.67/1.96 % (4064372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.67/1.96 % (4064372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.67/1.96 % (4064372)CaDiCaL version: 2.1.3
% 5.67/1.96 % (4064372)Termination reason: Refutation
% 5.67/1.96 % (4064372)Time elapsed: 0.056 s
% 5.67/1.96 % (4064372)Peak memory usage: 116 MB
% 5.67/1.96 % (4064372)Instructions burned: 18 (million)
% 5.67/1.96 % (4064372)------------------------------
% 5.67/1.96 % (4064372)------------------------------
% 5.67/1.96 % (4064364)Success in time 0.656 s
% 5.67/1.96 % Vampire exiting
%------------------------------------------------------------------------------