%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM504+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 : n010.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 12:15:29 PM UTC 2026
% Result : ContradictoryAxioms 3.56s 1.47s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 19 unt; 0 def)
% Number of atoms : 127 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 128 ( 47 ~; 36 |; 41 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 32 ( 24 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( ( sdtlseqdt0(X0,X1)
& sdtlseqdt0(X1,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f45,axiom,
( aNaturalNumber0(xk)
& sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
& xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(f49,axiom,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xr,X0) = xk )
& ? [X0] :
( aNaturalNumber0(X0)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X0) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xp,xm),X0) = sdtasdt0(xp,xk) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(f58,plain,
( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xr,X0) = xk )
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(rectify,[],[f49]) ).
fof(f59,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(sdtasdt0(xn,xm),X0) = sdtasdt0(xp,xm) )
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),X1) )
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(rectify,[],[f51]) ).
fof(f86,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f87,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f86]) ).
fof(f99,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f100,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f99]) ).
fof(f125,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f126,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X0,X1)
| ~ sdtlseqdt0(X1,X0)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f125]) ).
fof(f148,plain,
( aNaturalNumber0(sK10)
& xk = sdtpldt0(xr,sK10)
& aNaturalNumber0(sK11)
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK11)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f58]) ).
fof(f150,plain,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& aNaturalNumber0(sK13)
& sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK13)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& aNaturalNumber0(sK14)
& sdtasdt0(xp,xk) = sdtpldt0(sdtasdt0(xp,xm),sK14)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f59]) ).
fof(f165,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f166,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f204,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
inference(cnf_transformation,[],[f45]) ).
fof(f220,plain,
sdtasdt0(xn,xm) = sdtasdt0(xr,sK11),
inference(cnf_transformation,[],[f148]) ).
fof(f227,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(cnf_transformation,[],[f150]) ).
fof(f230,plain,
sdtasdt0(xp,xk) != sdtasdt0(xp,xm),
inference(cnf_transformation,[],[f150]) ).
fof(f231,plain,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(cnf_transformation,[],[f150]) ).
fof(f232,plain,
sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xn,xm),sK13),
inference(cnf_transformation,[],[f150]) ).
fof(f233,plain,
aNaturalNumber0(sK13),
inference(cnf_transformation,[],[f150]) ).
fof(f252,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f261,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f291,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f319,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm)),
inference(forward_demodulation,[],[f227,f204]) ).
fof(f320,plain,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xr,sK11)),
inference(forward_demodulation,[],[f319,f220]) ).
fof(f321,plain,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(forward_demodulation,[],[f230,f204]) ).
fof(f322,plain,
sdtasdt0(xp,xm) != sdtasdt0(xr,sK11),
inference(forward_demodulation,[],[f321,f220]) ).
fof(f323,plain,
sdtlseqdt0(sdtasdt0(xr,sK11),sdtasdt0(xp,xm)),
inference(forward_demodulation,[],[f231,f220]) ).
fof(f339,plain,
( aNaturalNumber0(sdtasdt0(xr,sK11))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[],[f261,f220]) ).
fof(f349,plain,
( aNaturalNumber0(sdtasdt0(xr,sK11))
| ~ aNaturalNumber0(xm) ),
inference(forward_subsumption_resolution,[],[f339,f166]) ).
fof(f352,plain,
aNaturalNumber0(sdtasdt0(xr,sK11)),
inference(forward_subsumption_resolution,[],[f349,f165]) ).
fof(f357,plain,
sdtasdt0(xp,xm) = sdtpldt0(sdtasdt0(xr,sK11),sK13),
inference(forward_demodulation,[],[f232,f220]) ).
fof(f359,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,sK11))
| ~ aNaturalNumber0(sK13) ),
inference(superposition,[],[f252,f357]) ).
fof(f360,plain,
( aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sK13) ),
inference(forward_subsumption_resolution,[],[f359,f352]) ).
fof(f361,plain,
aNaturalNumber0(sdtasdt0(xp,xm)),
inference(forward_subsumption_resolution,[],[f360,f233]) ).
fof(f746,plain,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xr,sK11))
| sdtasdt0(xp,xm) = sdtasdt0(xr,sK11)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,sK11)) ),
inference(resolution,[],[f291,f323]) ).
fof(f764,plain,
( sdtasdt0(xp,xm) = sdtasdt0(xr,sK11)
| ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,sK11)) ),
inference(forward_subsumption_resolution,[],[f746,f320]) ).
fof(f770,plain,
( ~ aNaturalNumber0(sdtasdt0(xp,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,sK11)) ),
inference(forward_subsumption_resolution,[],[f764,f322]) ).
fof(f772,plain,
~ aNaturalNumber0(sdtasdt0(xr,sK11)),
inference(forward_subsumption_resolution,[],[f770,f361]) ).
fof(f774,plain,
$false,
inference(forward_subsumption_resolution,[],[f772,f352]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM504+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.37 % Computer : n010.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sun Sep 27 20:14:02 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 3.56/1.47 % (1279317)Detected formulas, will run a generic FOF schedule.
% 3.56/1.47 % (1279352)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=1358444569:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.47 % (1279349)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=299257722:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.47 % (1279351)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=2091127235:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.47 % (1279353)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=784133770:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.47 % (1279356)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1268051103:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.47 % (1279354)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3673979364:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.47 % (1279358)dis-21_1_sil=8000:lcm=predicate:random_seed=1682497868: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)
% 3.56/1.47 % (1279354)First to succeed.
% 3.56/1.47 % (1279354)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1279317"
% 3.56/1.47 % (1279356)Also succeeded, but the first one will report.
% 3.56/1.47 % (1279353)Instruction limit reached!
% 3.56/1.47 % (1279353)------------------------------
% 3.56/1.47 % (1279353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (1279353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (1279353)CaDiCaL version: 2.1.3
% 3.56/1.47 % (1279353)Termination reason: Instruction limit
% 3.56/1.47 % (1279353)Termination phase: Saturation
% 3.56/1.47 % (1279353)Time elapsed: 0.062 s
% 3.56/1.47 % (1279353)Peak memory usage: 89 MB
% 3.56/1.47 % (1279353)Instructions burned: 110 (million)
% 3.56/1.47 % (1279358)Instruction limit reached!
% 3.56/1.47 % (1279358)------------------------------
% 3.56/1.47 % (1279358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (1279358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (1279358)CaDiCaL version: 2.1.3
% 3.56/1.47 % (1279358)Termination reason: Instruction limit
% 3.56/1.47 % (1279358)Termination phase: Saturation
% 3.56/1.47 % (1279358)Time elapsed: 0.078 s
% 3.56/1.47 % (1279358)Peak memory usage: 91 MB
% 3.56/1.47 % (1279358)Instructions burned: 129 (million)
% 3.56/1.47 % (1279420)lrs+10_1_sil=8000:sp=occurrence:random_seed=1747668695:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.56/1.47 % (1279420)Also succeeded, but the first one will report.
% 3.56/1.47 % (1279424)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3247882762:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.56/1.47 % (1279424)Refutation not found, incomplete strategy
% 3.56/1.47 % (1279424)------------------------------
% 3.56/1.47 % (1279424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (1279424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (1279424)CaDiCaL version: 2.1.3
% 3.56/1.47 % (1279424)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.47 % (1279424)Time elapsed: 0.001 s
% 3.56/1.47 % (1279424)Peak memory usage: 87 MB
% 3.56/1.47 % (1279424)Instructions burned: 1 (million)
% 3.56/1.47 % (1279354)Refutation found. Thanks to Tanya!
% 3.56/1.47 % SZS status ContradictoryAxioms for theBenchmark
% 3.56/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.47 % (1279354)------------------------------
% 3.56/1.47 % (1279354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (1279354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (1279354)CaDiCaL version: 2.1.3
% 3.56/1.47 % (1279354)Termination reason: Refutation
% 3.56/1.47 % (1279354)Time elapsed: 0.012 s
% 3.56/1.47 % (1279354)Peak memory usage: 88 MB
% 3.56/1.47 % (1279354)Instructions burned: 19 (million)
% 3.56/1.47 % (1279354)------------------------------
% 3.56/1.47 % (1279354)------------------------------
% 3.56/1.47 % (1279317)Success in time 0.42 s
% 3.56/1.47 % Vampire exiting
%------------------------------------------------------------------------------