%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:15:04 PM UTC 2026
% Result : Theorem 3.40s 11.49s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 32 ~; 25 |; 9 &)
% ( 2 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 31 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f26,axiom,
! [X0] :
? [X1] :
! [X2] :
( in(X2,X1)
<=> ( in(X2,X0)
& ordinal(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).
fof(f29,axiom,
! [X0] :
~ ! [X1] :
( in(X1,X0)
<=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_ordinal1) ).
fof(f30,conjecture,
! [X0] :
~ ! [X1] :
( ordinal(X1)
=> in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_ordinal1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
~ ! [X1] :
( ordinal(X1)
=> in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f35,plain,
? [X0] :
! [X1] :
( in(X1,X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f37,plain,
! [X0] :
? [X1] :
( in(X1,X0)
<~> ordinal(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f39,plain,
! [X1] :
( in(X1,sK0)
| ~ ordinal(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f35]) ).
fof(f40,plain,
! [X0] :
? [X1] :
( ( ~ ordinal(X1)
| ~ in(X1,X0) )
& ( ordinal(X1)
| in(X1,X0) ) ),
inference(nnf_transformation,[],[f37]) ).
fof(f41,plain,
! [X0] :
( ( ~ ordinal(sK1(X0))
| ~ in(sK1(X0),X0) )
& ( ordinal(sK1(X0))
| in(sK1(X0),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f40]) ).
fof(f42,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,X1) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0] :
? [X1] :
! [X2] :
( ( in(X2,X1)
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,X1) ) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X2] :
( ( in(X2,sK2(X0))
| ~ in(X2,X0)
| ~ ordinal(X2) )
& ( ( in(X2,X0)
& ordinal(X2) )
| ~ in(X2,sK2(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f43]) ).
fof(f47,plain,
! [X1] :
( in(X1,sK0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0] :
( in(sK1(X0),X0)
| ordinal(sK1(X0)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f50,plain,
! [X0] :
( ~ in(sK1(X0),X0)
| ~ ordinal(sK1(X0)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f51,plain,
! [X2,X0] :
( ~ in(X2,sK2(X0))
| ordinal(X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f53,plain,
! [X2,X0] :
( in(X2,sK2(X0))
| ~ in(X2,X0)
| ~ ordinal(X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f64,plain,
! [X0] :
( ordinal(sK1(sK2(X0)))
| ordinal(sK1(sK2(X0))) ),
inference(resolution,[],[f49,f51]) ).
fof(f65,plain,
! [X0] : ordinal(sK1(sK2(X0))),
inference(duplicate_literal_removal,[],[f64]) ).
fof(f78,plain,
! [X0] :
( ~ in(sK1(sK2(X0)),X0)
| ~ ordinal(sK1(sK2(X0)))
| ~ ordinal(sK1(sK2(X0))) ),
inference(resolution,[],[f53,f50]) ).
fof(f79,plain,
! [X0] :
( ~ in(sK1(sK2(X0)),X0)
| ~ ordinal(sK1(sK2(X0))) ),
inference(duplicate_literal_removal,[],[f78]) ).
fof(f80,plain,
! [X0] : ~ in(sK1(sK2(X0)),X0),
inference(forward_subsumption_resolution,[],[f79,f65]) ).
fof(f83,plain,
~ ordinal(sK1(sK2(sK0))),
inference(resolution,[],[f80,f47]) ).
fof(f86,plain,
$false,
inference(forward_subsumption_resolution,[],[f83,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM405+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.62 % Computer : n008.cluster.edu
% 0.13/10.62 % Model : x86_64 x86_64
% 0.13/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.62 % Memory : 8046.5625MB
% 0.13/10.62 % OS : Linux 6.8.0-71-generic
% 0.13/10.62 % CPULimit : 300
% 0.13/10.62 % WCLimit : 300
% 0.13/10.62 % DateTime : Sun Sep 27 19:48:08 UTC 2026
% 0.13/10.62 % CPUTime :
% 0.13/10.62 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/10.65 Running first-order theorem proving
% 0.13/10.65 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
% 3.40/11.49 % (1555146)Detected formulas, will run a generic FOF schedule.
% 3.40/11.49 % (1555152)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=587693693:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.40/11.49 % (1555155)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=632146136:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.40/11.49 % (1555154)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=142926715:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.40/11.49 % (1555156)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4190628795:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.40/11.49 % (1555157)dis-21_1_sil=8000:lcm=predicate:random_seed=2299413241: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)
% 3.40/11.49 % (1555151)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=4080775882:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.40/11.49 % (1555153)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=1789853529:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.40/11.49 % (1555154)Refutation not found, incomplete strategy
% 3.40/11.49 % (1555154)------------------------------
% 3.40/11.49 % (1555154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/11.49 % (1555155)First to succeed.
% 3.40/11.49 % (1555154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/11.49 % (1555154)CaDiCaL version: 2.1.3
% 3.40/11.49 % (1555154)Termination reason: Refutation not found, incomplete strategy
% 3.40/11.49 % (1555154)Time elapsed: 0.001 s
% 3.40/11.49 % (1555154)Peak memory usage: 88 MB
% 3.40/11.49 % (1555155)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1555146"
% 3.40/11.49 % (1555156)Also succeeded, but the first one will report.
% 3.40/11.49 % (1555157)Instruction limit reached!
% 3.40/11.49 % (1555157)------------------------------
% 3.40/11.49 % (1555157)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/11.49 % (1555157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/11.49 % (1555157)CaDiCaL version: 2.1.3
% 3.40/11.49 % (1555157)Termination reason: Instruction limit
% 3.40/11.49 % (1555157)Termination phase: Saturation
% 3.40/11.49 % (1555157)Time elapsed: 0.064 s
% 3.40/11.49 % (1555157)Peak memory usage: 89 MB
% 3.40/11.49 % (1555157)Instructions burned: 131 (million)
% 3.40/11.49 % (1555165)lrs+10_1_sil=8000:sp=occurrence:random_seed=3873180432:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.40/11.49 % (1555154)------------------------------
% 3.40/11.49 % (1555154)------------------------------
% 3.40/11.49 % (1555165)Also succeeded, but the first one will report.
% 3.40/11.49 % (1555155)Refutation found. Thanks to Tanya!
% 3.40/11.49 % SZS status Theorem for theBenchmark
% 3.40/11.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/11.49 % (1555155)------------------------------
% 3.40/11.49 % (1555155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/11.49 % (1555155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/11.49 % (1555155)CaDiCaL version: 2.1.3
% 3.40/11.49 % (1555155)Termination reason: Refutation
% 3.40/11.49 % (1555155)Time elapsed: 0.002 s
% 3.40/11.49 % (1555155)Peak memory usage: 88 MB
% 3.40/11.49 % (1555155)Instructions burned: 1 (million)
% 3.40/11.49 % (1555155)------------------------------
% 3.40/11.49 % (1555155)------------------------------
% 3.40/11.49 % (1555146)Success in time 0.426 s
% 3.40/11.49 % Vampire exiting
%------------------------------------------------------------------------------