%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 : Theorem 0.14s 1.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 101 ( 37 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 123 ( 52 ~; 38 |; 28 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 18 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X0)
& aNaturalNumber0(X1) )
=> ( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f39,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',m__2306) ).
fof(f50,conjecture,
( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f51,negated_conjecture,
~ ( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xk,X0) = xp )
| sdtlseqdt0(xk,xp) ) ) ),
inference(negated_conjecture,[status(cth)],[f50]) ).
fof(f57,plain,
~ ( ~ ( ? [X0] :
( aNaturalNumber0(X0)
& sdtpldt0(xp,X0) = xk )
| sdtlseqdt0(xp,xk) )
=> ( xk != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& xp = sdtpldt0(xk,X1) )
| sdtlseqdt0(xk,xp) ) ) ),
inference(rectify,[],[f51]) ).
fof(f69,plain,
( ( xp = xk
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xk,X1) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) != xk )
& ~ sdtlseqdt0(xp,xk) ),
inference(ennf_transformation,[],[f57]) ).
fof(f70,plain,
( ( xp = xk
| ( ! [X1] :
( ~ aNaturalNumber0(X1)
| xp != sdtpldt0(xk,X1) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(xp,X0) != xk )
& ~ sdtlseqdt0(xp,xk) ),
inference(flattening,[],[f69]) ).
fof(f80,plain,
! [X0] :
( ( sdtpldt0(X0,sz00) = X0
& X0 = sdtpldt0(sz00,X0) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f120,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f121,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| ( X1 != X0
& sdtlseqdt0(X1,X0) )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(flattening,[],[f120]) ).
fof(f148,plain,
( ( xp = xk
| ( ! [X0] :
( ~ aNaturalNumber0(X0)
| xp != sdtpldt0(xk,X0) )
& ~ sdtlseqdt0(xk,xp) ) )
& ! [X1] :
( ~ aNaturalNumber0(X1)
| xk != sdtpldt0(xp,X1) )
& ~ sdtlseqdt0(xp,xk) ),
inference(rectify,[],[f70]) ).
fof(f162,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f203,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[],[f45]) ).
fof(f222,plain,
~ sdtlseqdt0(xp,xk),
inference(cnf_transformation,[],[f148]) ).
fof(f223,plain,
! [X1] :
( xk != sdtpldt0(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f148]) ).
fof(f224,plain,
( ~ sdtlseqdt0(xk,xp)
| xp = xk ),
inference(cnf_transformation,[],[f148]) ).
fof(f226,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f240,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f279,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f308,plain,
( xp != xk
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[],[f223,f240]) ).
fof(f310,plain,
( xp != xk
| ~ aNaturalNumber0(xp) ),
inference(forward_subsumption_resolution,[],[f308,f226]) ).
fof(f311,plain,
xp != xk,
inference(forward_subsumption_resolution,[],[f310,f162]) ).
fof(f352,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk ),
inference(resolution,[],[f279,f224]) ).
fof(f353,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk)
| xp = xk ),
inference(forward_subsumption_resolution,[],[f352,f222]) ).
fof(f355,plain,
( ~ aNaturalNumber0(xk)
| xp = xk ),
inference(forward_subsumption_resolution,[],[f353,f162]) ).
fof(f357,plain,
xp = xk,
inference(forward_subsumption_resolution,[],[f355,f203]) ).
fof(f358,plain,
$false,
inference(forward_subsumption_resolution,[],[f357,f311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM505+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.40 % Computer : n001.cluster.edu
% 0.08/0.40 % Model : x86_64 x86_64
% 0.08/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.40 % Memory : 8046.5625MB
% 0.08/0.40 % OS : Linux 6.8.0-71-generic
% 0.08/0.40 % CPULimit : 300
% 0.08/0.40 % WCLimit : 300
% 0.08/0.40 % DateTime : Sun Sep 27 20:20:47 UTC 2026
% 0.08/0.40 % CPUTime :
% 0.08/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.44 Running first-order theorem proving
% 0.08/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/1.40 % (3922681)Detected formulas, will run a generic FOF schedule.
% 0.14/1.40 % (3922686)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=1656580803:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.14/1.40 % (3922690)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1383357709:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.14/1.40 % (3922687)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=1724365853:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.14/1.40 % (3922692)dis-21_1_sil=8000:lcm=predicate:random_seed=628717301: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)
% 0.14/1.40 % (3922689)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=168164349:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.14/1.40 % (3922688)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=3200164764:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.14/1.40 % (3922691)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=25697501:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.14/1.40 % (3922690)First to succeed.
% 0.14/1.40 % (3922690)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3922681"
% 0.14/1.40 % (3922691)Also succeeded, but the first one will report.
% 0.14/1.40 % (3922689)Also succeeded, but the first one will report.
% 0.14/1.40 % (3922692)Instruction limit reached!
% 0.14/1.40 % (3922692)------------------------------
% 0.14/1.40 % (3922692)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (3922692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (3922692)CaDiCaL version: 2.1.3
% 0.14/1.40 % (3922692)Termination reason: Instruction limit
% 0.14/1.40 % (3922692)Termination phase: Saturation
% 0.14/1.40 % (3922692)Time elapsed: 0.078 s
% 0.14/1.40 % (3922692)Peak memory usage: 91 MB
% 0.14/1.40 % (3922692)Instructions burned: 129 (million)
% 0.14/1.40 % (3922700)lrs+10_1_sil=8000:sp=occurrence:random_seed=3383542040:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 0.14/1.40 % (3922700)Also succeeded, but the first one will report.
% 0.14/1.40 % (3922690)Refutation found. Thanks to Tanya!
% 0.14/1.40 % SZS status Theorem for theBenchmark
% 0.14/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.40 % (3922690)------------------------------
% 0.14/1.40 % (3922690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.40 % (3922690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.40 % (3922690)CaDiCaL version: 2.1.3
% 0.14/1.40 % (3922690)Termination reason: Refutation
% 0.14/1.40 % (3922690)Time elapsed: 0.006 s
% 0.14/1.40 % (3922690)Peak memory usage: 88 MB
% 0.14/1.40 % (3922690)Instructions burned: 8 (million)
% 0.14/1.40 % (3922690)------------------------------
% 0.14/1.40 % (3922690)------------------------------
% 0.14/1.40 % (3922681)Success in time 0.423 s
% 0.14/1.40 % Vampire exiting
%------------------------------------------------------------------------------