%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM532+1 : 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 : 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 12:15:37 PM UTC 2026
% Result : Theorem 3.65s 1.47s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 88 ( 36 ~; 34 |; 14 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(f12,axiom,
aSet0(xA),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__467) ).
fof(f13,conjecture,
aSubsetOf0(xA,xA),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f14,negated_conjecture,
~ aSubsetOf0(xA,xA),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
~ aSubsetOf0(xA,xA),
inference(flattening,[],[f14]) ).
fof(f20,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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,[],[f21]) ).
fof(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK0(X0,X1),X0)
& aElementOf0(sK0(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f23]) ).
fof(f25,plain,
aSet0(xA),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
~ aSubsetOf0(xA,xA),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( aElementOf0(sK0(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f31,plain,
! [X0,X1] :
( ~ aElementOf0(sK0(X0,X1),X0)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X0] :
( ~ aSet0(X0)
| aSubsetOf0(X0,X0)
| ~ aSet0(X0)
| ~ aSet0(X0)
| aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f31,f30]) ).
fof(f35,plain,
! [X0] :
( aSubsetOf0(X0,X0)
| ~ aSet0(X0) ),
inference(duplicate_literal_removal,[],[f32]) ).
fof(f36,plain,
~ aSet0(xA),
inference(resolution,[],[f35,f26]) ).
fof(f41,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM532+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 20:22:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.65/1.47 % (1575355)Detected formulas, will run a generic FOF schedule.
% 3.65/1.47 % (1575364)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2109994629:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.47 % (1575364)Refutation not found, incomplete strategy
% 3.65/1.47 % (1575364)------------------------------
% 3.65/1.47 % (1575364)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.47 % (1575364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.47 % (1575364)CaDiCaL version: 2.1.3
% 3.65/1.47 % (1575364)Termination reason: Refutation not found, incomplete strategy
% 3.65/1.47 % (1575364)Time elapsed: 0.001 s
% 3.65/1.47 % (1575364)Peak memory usage: 88 MB
% 3.65/1.47 % (1575363)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=13379240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.47 % (1575365)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1604343667:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.47 % (1575361)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=525559722:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.47 % (1575367)dis-21_1_sil=8000:lcm=predicate:random_seed=3868939002: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)
% 3.65/1.47 % (1575362)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=2261008628:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.47 % (1575366)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=44855439:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.47 % (1575365)First to succeed.
% 3.65/1.47 % (1575366)Also succeeded, but the first one will report.
% 3.65/1.47 % (1575365)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1575355"
% 3.65/1.47 % (1575367)Also succeeded, but the first one will report.
% 3.65/1.47 % (1575364)------------------------------
% 3.65/1.47 % (1575364)------------------------------
% 3.65/1.47 % (1575375)lrs+10_1_sil=8000:sp=occurrence:random_seed=1852896296:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.65/1.47 % (1575375)Also succeeded, but the first one will report.
% 3.65/1.47 % (1575365)Refutation found. Thanks to Tanya!
% 3.65/1.47 % SZS status Theorem for theBenchmark
% 3.65/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.47 % (1575365)------------------------------
% 3.65/1.47 % (1575365)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.47 % (1575365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.47 % (1575365)CaDiCaL version: 2.1.3
% 3.65/1.47 % (1575365)Termination reason: Refutation
% 3.65/1.47 % (1575365)Time elapsed: 0.002 s
% 3.65/1.47 % (1575365)Peak memory usage: 88 MB
% 3.65/1.47 % (1575365)Instructions burned: 1 (million)
% 3.65/1.47 % (1575365)------------------------------
% 3.65/1.47 % (1575365)------------------------------
% 3.65/1.47 % (1575355)Success in time 0.433 s
% 3.65/1.47 % Vampire exiting
%------------------------------------------------------------------------------