%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM533+1 : 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 : n002.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 12:15:37 PM UTC 2026
% Result : Theorem 4.05s 1.47s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 171 ( 73 ~; 70 |; 22 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 49 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
fof(f15,conjecture,
( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f31,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(ennf_transformation,[],[f16]) ).
fof(f32,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(flattening,[],[f31]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK1(X0,X1),X0)
& aElementOf0(sK1(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f39]) ).
fof(f45,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f46,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f48,plain,
! [X0,X1] :
( ~ aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
aSet0(xC),
inference(cnf_transformation,[],[f14]) ).
fof(f54,plain,
aSet0(xA),
inference(cnf_transformation,[],[f14]) ).
fof(f55,plain,
aSubsetOf0(xB,xC),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
aSubsetOf0(xA,xB),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
~ aSubsetOf0(xA,xC),
inference(cnf_transformation,[],[f32]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X1,X0),X2)
| ~ aSubsetOf0(X2,X1)
| ~ aSet0(X1) ),
inference(resolution,[],[f48,f45]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ aElementOf0(sK1(X1,X0),X2)
| aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X1) ),
inference(duplicate_literal_removal,[],[f68]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( aSubsetOf0(X0,X1)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X1)
| ~ aElementOf0(sK1(X1,X0),X3)
| ~ aSubsetOf0(X3,X2)
| ~ aSet0(X2) ),
inference(resolution,[],[f69,f45]) ).
fof(f106,plain,
! [X2,X3,X0,X1] :
( ~ aElementOf0(sK1(X1,X0),X3)
| ~ aSet0(X1)
| ~ aSet0(X0)
| ~ aSubsetOf0(X2,X1)
| aSubsetOf0(X0,X1)
| ~ aSubsetOf0(X3,X2) ),
inference(forward_subsumption_resolution,[],[f104,f46]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ aSet0(X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| aSubsetOf0(X1,X0)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f106,f47]) ).
fof(f109,plain,
! [X2,X0,X1] :
( ~ aSubsetOf0(X1,X2)
| ~ aSet0(X1)
| ~ aSubsetOf0(X2,X0)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(duplicate_literal_removal,[],[f107]) ).
fof(f112,plain,
! [X0] :
( ~ aSet0(xA)
| ~ aSubsetOf0(xB,X0)
| aSubsetOf0(xA,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f109,f56]) ).
fof(f118,plain,
! [X0] :
( ~ aSubsetOf0(xB,X0)
| aSubsetOf0(xA,X0)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[],[f112,f54]) ).
fof(f127,plain,
( aSubsetOf0(xA,xC)
| ~ aSet0(xC) ),
inference(resolution,[],[f118,f55]) ).
fof(f130,plain,
~ aSet0(xC),
inference(forward_subsumption_resolution,[],[f127,f57]) ).
fof(f131,plain,
$false,
inference(forward_subsumption_resolution,[],[f130,f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM533+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n002.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 20:24:52 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 4.05/1.47 % (3851219)Detected formulas, will run a generic FOF schedule.
% 4.05/1.47 % (3851230)dis-21_1_sil=8000:lcm=predicate:random_seed=3183546464: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)
% 4.05/1.47 % (3851230)Instruction limit reached!
% 4.05/1.47 % (3851230)------------------------------
% 4.05/1.47 % (3851230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.47 % (3851230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.47 % (3851230)CaDiCaL version: 2.1.3
% 4.05/1.47 % (3851230)Termination reason: Instruction limit
% 4.05/1.47 % (3851230)Termination phase: Saturation
% 4.05/1.47 % (3851230)Time elapsed: 0.030 s
% 4.05/1.47 % (3851230)Peak memory usage: 88 MB
% 4.05/1.47 % (3851230)Instructions burned: 135 (million)
% 4.05/1.47 % (3851227)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1899652473:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.05/1.47 % (3851226)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=1294667674:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.05/1.47 % (3851224)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=519195194:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.05/1.47 % (3851228)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=110235117:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.05/1.47 % (3851225)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=4029433551:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.05/1.47 % (3851227)Refutation not found, incomplete strategy
% 4.05/1.47 % (3851227)------------------------------
% 4.05/1.47 % (3851227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.47 % (3851227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.47 % (3851228)Refutation not found, incomplete strategy
% 4.05/1.47 % (3851228)------------------------------
% 4.05/1.47 % (3851228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.47 % (3851227)CaDiCaL version: 2.1.3
% 4.05/1.47 % (3851227)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.47 % (3851227)Time elapsed: 0.001 s
% 4.05/1.47 % (3851228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.47 % (3851227)Peak memory usage: 87 MB
% 4.05/1.47 % (3851228)CaDiCaL version: 2.1.3
% 4.05/1.47 % (3851228)Termination reason: Refutation not found, incomplete strategy
% 4.05/1.47 % (3851228)Time elapsed: 0.001 s
% 4.05/1.47 % (3851228)Peak memory usage: 87 MB
% 4.05/1.47 % (3851229)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3838191637:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.05/1.47 % (3851229)First to succeed.
% 4.05/1.47 % (3851229)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3851219"
% 4.05/1.47 % (3851237)lrs+10_1_sil=8000:sp=occurrence:random_seed=1153778204:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.05/1.47 % (3851237)Also succeeded, but the first one will report.
% 4.05/1.47 % (3851228)------------------------------
% 4.05/1.47 % (3851228)------------------------------
% 4.05/1.47 % (3851227)------------------------------
% 4.05/1.47 % (3851227)------------------------------
% 4.05/1.47 % (3851229)Refutation found. Thanks to Tanya!
% 4.05/1.47 % SZS status Theorem for theBenchmark
% 4.05/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.47 % (3851229)------------------------------
% 4.05/1.47 % (3851229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.47 % (3851229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.47 % (3851229)CaDiCaL version: 2.1.3
% 4.05/1.47 % (3851229)Termination reason: Refutation
% 4.05/1.47 % (3851229)Time elapsed: 0.004 s
% 4.05/1.47 % (3851229)Peak memory usage: 89 MB
% 4.05/1.47 % (3851229)Instructions burned: 3 (million)
% 4.05/1.47 % (3851229)------------------------------
% 4.05/1.47 % (3851229)------------------------------
% 4.05/1.47 % (3851219)Success in time 0.519 s
% 4.05/1.47 % Vampire exiting
%------------------------------------------------------------------------------