%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM900_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:17:24 PM UTC 2026
% Result : Theorem 3.79s 6.50s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 35 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 7 ~; 0 |; 10 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 72 ( 19 atm; 22 fun; 13 num; 18 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 3 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 12 !; 6 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $int ).
tff(func_def_6,type,
sK1: $int ).
tff(func_def_7,type,
sK2: $int ).
tff(f1,conjecture,
! [X2: $int,X0: $int,X1: $int] :
( ( $less(0,X2)
& ( $difference(X0,X1) = X2 ) )
=> $less(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_greater) ).
tff(f2,negated_conjecture,
~ ! [X2: $int,X0: $int,X1: $int] :
( ( $less(0,X2)
& ( $difference(X0,X1) = X2 ) )
=> $less(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X2: $int,X0: $int,X1: $int] :
( ( $less(0,X2)
& ( $sum(X0,$uminus(X1)) = X2 ) )
=> $less(X1,X0) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ! [X0: $int,X2: $int,X1: $int] :
( ( $less(0,X0)
& ( $sum(X1,$uminus(X2)) = X0 ) )
=> $less(X2,X1) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
? [X0: $int,X2: $int,X1: $int] :
( ~ $less(X2,X1)
& $less(0,X0)
& ( $sum(X1,$uminus(X2)) = X0 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
? [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,X1)
& ( $sum(X1,$uminus(X2)) = X0 )
& $less(0,X0) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ~ $less(sK2,sK1)
& ( sK0 = $sum(sK1,$uminus(sK2)) )
& $less(0,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18]) ).
tff(f20,plain,
$less(0,sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
sK0 = $sum(sK1,$uminus(sK2)),
inference(cnf_transformation,[],[f19]) ).
tff(f22,plain,
~ $less(sK2,sK1),
inference(cnf_transformation,[],[f19]) ).
tff(f23,plain,
$less(0,$sum($sum(sK2,1),$uminus(sK1))),
inference(evaluation,[],[f22]) ).
tff(f25,definition,
( spl3_1
<=> $less(0,$sum($sum(sK2,1),$uminus(sK1))) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f28,plain,
spl3_1,
inference(avatar_split_clause,[],[f23,f25]) ).
tff(f30,definition,
( spl3_2
<=> $less(0,sK0) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f33,plain,
spl3_2,
inference(avatar_split_clause,[],[f20,f30]) ).
tff(f35,definition,
( spl3_3
<=> ( sK0 = $sum(sK1,$uminus(sK2)) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f38,plain,
spl3_3,
inference(avatar_split_clause,[],[f21,f35]) ).
tff(f39,plain,
$false,
inference(avatar_smt_refutation,[],[f38,f33,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM900_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/5.37 % Computer : n026.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sun Sep 27 21:41:32 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 Running first-order theorem proving
% 0.13/5.40 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
% 3.79/6.50 % (3229237)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.79/6.50 % (3229245)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3488624785:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.79/6.50 % (3229245)Instruction limit reached!
% 3.79/6.50 % (3229245)------------------------------
% 3.79/6.50 % (3229245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/6.50 % (3229245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/6.50 % (3229245)CaDiCaL version: 2.1.3
% 3.79/6.50 % (3229245)Termination reason: Instruction limit
% 3.79/6.50 % (3229245)Termination phase: Saturation
% 3.79/6.50 % (3229245)Time elapsed: 0.004 s
% 3.79/6.50 % (3229245)Peak memory usage: 88 MB
% 3.79/6.50 % (3229245)Instructions burned: 10 (million)
% 3.79/6.50 % (3229248)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1641660802:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.79/6.50 % (3229243)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=644643831:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.79/6.50 % (3229246)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3635549328:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.79/6.50 % (3229247)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1429855623:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.79/6.50 % (3229242)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3661483743:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.79/6.50 % (3229244)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1268573120:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.79/6.50 % (3229246)Instruction limit reached!
% 3.79/6.50 % (3229246)------------------------------
% 3.79/6.50 % (3229246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/6.50 % (3229246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/6.50 % (3229246)CaDiCaL version: 2.1.3
% 3.79/6.50 % (3229246)Termination reason: Instruction limit
% 3.79/6.50 % (3229246)Termination phase: Saturation
% 3.79/6.50 % (3229246)Time elapsed: 0.004 s
% 3.79/6.50 % (3229246)Peak memory usage: 88 MB
% 3.79/6.50 % (3229246)Instructions burned: 4 (million)
% 3.79/6.50 % (3229247)Also succeeded, but the first one will report.
% 3.79/6.50 % (3229242)First to succeed.
% 3.79/6.50 % (3229243)Also succeeded, but the first one will report.
% 3.79/6.50 % (3229248)Also succeeded, but the first one will report.
% 3.79/6.50 % (3229242)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3229237"
% 3.79/6.50 % (3229250)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2987275260:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.79/6.50 % (3229250)Refutation not found, incomplete strategy
% 3.79/6.50 % (3229250)------------------------------
% 3.79/6.50 % (3229250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/6.50 % (3229250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/6.50 % (3229250)CaDiCaL version: 2.1.3
% 3.79/6.50 % (3229250)Termination reason: Refutation not found, incomplete strategy
% 3.79/6.50 % (3229250)Time elapsed: 0.001 s
% 3.79/6.50 % (3229250)Peak memory usage: 89 MB
% 3.79/6.50 % (3229244)Also succeeded, but the first one will report.
% 3.79/6.50 % (3229257)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=3005158437:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.79/6.50 % (3229257)Instruction limit reached!
% 3.79/6.50 % (3229257)------------------------------
% 3.79/6.50 % (3229257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/6.50 % (3229257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/6.50 % (3229257)CaDiCaL version: 2.1.3
% 3.79/6.50 % (3229257)Termination reason: Instruction limit
% 3.79/6.50 % (3229257)Termination phase: Saturation
% 3.79/6.50 % (3229257)Time elapsed: 0.020 s
% 3.79/6.50 % (3229257)Peak memory usage: 89 MB
% 3.79/6.50 % (3229257)Instructions burned: 30 (million)
% 3.79/6.50 % (3229250)------------------------------
% 3.79/6.50 % (3229250)------------------------------
% 3.79/6.50 % (3229261)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1042976860:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 3.79/6.50 % (3229261)Instruction limit reached!
% 3.79/6.50 % (3229261)------------------------------
% 3.79/6.50 % (3229261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/6.50 % (3229261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/6.50 % (3229261)CaDiCaL version: 2.1.3
% 3.79/6.50 % (3229261)Termination reason: Instruction limit
% 3.79/6.50 % (3229261)Termination phase: Saturation
% 3.79/6.50 % (3229261)Time elapsed: 0.009 s
% 3.79/6.50 % (3229261)Peak memory usage: 89 MB
% 3.79/6.50 % (3229261)Instructions burned: 24 (million)
% 3.79/6.50 % (3229260)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3651739196:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 3.79/6.50 % (3229242)Refutation found. Thanks to Tanya!
% 3.79/6.50 % SZS status Theorem for theBenchmark
% 3.79/6.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/6.50 % (3229242)------------------------------
% 3.88/6.50 % (3229242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/6.50 % (3229242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/6.50 % (3229242)CaDiCaL version: 2.1.3
% 3.88/6.50 % (3229242)Termination reason: Refutation
% 3.88/6.50 % (3229242)Time elapsed: 0.032 s
% 3.88/6.50 % (3229242)Peak memory usage: 115 MB
% 3.88/6.50 % (3229242)Instructions burned: 9 (million)
% 3.88/6.50 % (3229242)------------------------------
% 3.88/6.50 % (3229242)------------------------------
% 3.88/6.50 % (3229237)Success in time 0.454 s
% 3.88/6.50 % Vampire exiting
%------------------------------------------------------------------------------