%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 12:15:07 PM UTC 2026
% Result : Theorem 2.63s 1.31s
% Output : Refutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 49 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 16 |; 10 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f20,axiom,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__671) ).
fof(f21,conjecture,
( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f22,negated_conjecture,
~ ( ? [X0] :
( aInteger0(X0)
& sdtasdt0(xq,X0) = sdtpldt0(xa,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f24,plain,
( ! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(ennf_transformation,[],[f22]) ).
fof(f27,plain,
! [X0] :
( ( sdtasdt0(X0,sz00) = sz00
& sz00 = sdtasdt0(sz00,X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00
& sz00 = sdtpldt0(smndt0(X0),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f54,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f20]) ).
fof(f55,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f20]) ).
fof(f58,plain,
! [X0] :
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f61,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f64,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f71,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f95,plain,
! [X0] :
( sz00 != sdtasdt0(xq,X0)
| ~ aInteger0(X0)
| ~ aInteger0(xa) ),
inference(superposition,[],[f58,f71]) ).
fof(f98,plain,
! [X0] :
( sz00 != sdtasdt0(xq,X0)
| ~ aInteger0(X0) ),
inference(forward_subsumption_resolution,[],[f95,f55]) ).
fof(f107,plain,
( sz00 != sz00
| ~ aInteger0(sz00)
| ~ aInteger0(xq) ),
inference(superposition,[],[f98,f61]) ).
fof(f108,plain,
( ~ aInteger0(sz00)
| ~ aInteger0(xq) ),
inference(trivial_inequality_removal,[],[f107]) ).
fof(f109,plain,
~ aInteger0(xq),
inference(forward_subsumption_resolution,[],[f108,f64]) ).
fof(f110,plain,
$false,
inference(forward_subsumption_resolution,[],[f109,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM423+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 19:46:05 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 2.63/1.31 % (2896805)Detected formulas, will run a generic FOF schedule.
% 2.63/1.31 % (2896814)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3167271308:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.63/1.31 % (2896814)First to succeed.
% 2.63/1.31 % (2896814)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2896805"
% 2.63/1.31 % (2896811)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=469900769:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.63/1.31 % (2896810)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=458343974:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.63/1.31 % (2896812)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3472034868:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.63/1.31 % (2896813)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1487558931:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.63/1.31 % (2896813)Also succeeded, but the first one will report.
% 2.63/1.31 % (2896816)dis-21_1_sil=8000:lcm=predicate:random_seed=455693566:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.63/1.31 % (2896815)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3559774774:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.63/1.31 % (2896816)Refutation not found, incomplete strategy
% 2.63/1.31 % (2896816)------------------------------
% 2.63/1.31 % (2896816)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.31 % (2896816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.31 % (2896816)CaDiCaL version: 2.1.3
% 2.63/1.31 % (2896816)Termination reason: Refutation not found, incomplete strategy
% 2.63/1.31 % (2896816)Time elapsed: 0.004 s
% 2.63/1.31 % (2896816)Peak memory usage: 88 MB
% 2.63/1.31 % (2896816)Instructions burned: 3 (million)
% 2.63/1.31 % (2896815)Also succeeded, but the first one will report.
% 2.63/1.31 % (2896814)Refutation found. Thanks to Tanya!
% 2.63/1.31 % SZS status Theorem for theBenchmark
% 2.63/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.63/1.32 % (2896814)------------------------------
% 2.63/1.32 % (2896814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.63/1.32 % (2896814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.63/1.32 % (2896814)CaDiCaL version: 2.1.3
% 2.63/1.32 % (2896814)Termination reason: Refutation
% 2.63/1.32 % (2896814)Time elapsed: 0.002 s
% 2.63/1.32 % (2896814)Peak memory usage: 88 MB
% 2.63/1.32 % (2896814)Instructions burned: 2 (million)
% 2.63/1.32 % (2896814)------------------------------
% 2.63/1.32 % (2896814)------------------------------
% 2.63/1.32 % (2896805)Success in time 0.287 s
% 2.63/1.32 % Vampire exiting
%------------------------------------------------------------------------------