%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM617+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 : 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 12:16:00 PM UTC 2026
% Result : Theorem 2.53s 1.31s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 96 ( 43 ~; 34 |; 15 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 27 !; 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(f23,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
fof(f101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f113,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
fof(f114,conjecture,
aElementOf0(xx,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f115,negated_conjecture,
~ aElementOf0(xx,szNzAzT0),
inference(negated_conjecture,[status(cth)],[f114]) ).
fof(f116,plain,
~ aElementOf0(xx,szNzAzT0),
inference(flattening,[],[f115]) ).
fof(f157,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f245,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,[],[f157]) ).
fof(f246,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,[],[f245]) ).
fof(f247,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,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK10(X0,X1),X0)
& aElementOf0(sK10(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f247]) ).
fof(f347,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(cnf_transformation,[],[f101]) ).
fof(f354,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f362,plain,
aElementOf0(xx,xP),
inference(cnf_transformation,[],[f113]) ).
fof(f363,plain,
~ aElementOf0(xx,szNzAzT0),
inference(cnf_transformation,[],[f116]) ).
fof(f366,plain,
aSet0(szNzAzT0),
inference(cnf_transformation,[],[f23]) ).
fof(f371,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f372,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f533,plain,
( aSet0(xQ)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f372,f347]) ).
fof(f537,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f533,f366]) ).
fof(f705,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,szNzAzT0)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[],[f371,f363]) ).
fof(f707,plain,
! [X0] :
( ~ aSubsetOf0(X0,szNzAzT0)
| ~ aElementOf0(xx,X0) ),
inference(forward_subsumption_resolution,[],[f705,f366]) ).
fof(f719,plain,
~ aElementOf0(xx,xQ),
inference(resolution,[],[f707,f347]) ).
fof(f723,plain,
! [X0] :
( ~ aElementOf0(xx,X0)
| ~ aSubsetOf0(X0,xQ)
| ~ aSet0(xQ) ),
inference(resolution,[],[f719,f371]) ).
fof(f724,plain,
! [X0] :
( ~ aSubsetOf0(X0,xQ)
| ~ aElementOf0(xx,X0) ),
inference(forward_subsumption_resolution,[],[f723,f537]) ).
fof(f750,plain,
~ aElementOf0(xx,xP),
inference(resolution,[],[f724,f354]) ).
fof(f751,plain,
$false,
inference(forward_subsumption_resolution,[],[f750,f362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM617+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 20:46:32 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.53/1.31 % (1294836)Detected formulas, will run a generic FOF schedule.
% 2.53/1.31 % (1294845)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3226005642:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/1.31 % (1294845)First to succeed.
% 2.53/1.31 % (1294845)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1294836"
% 2.53/1.31 % (1294841)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=2527056809:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/1.31 % (1294846)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2041061279:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/1.31 % (1294842)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=2897088859:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/1.31 % (1294843)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=3123870497:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/1.31 % (1294847)dis-21_1_sil=8000:lcm=predicate:random_seed=3570073005: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)
% 2.53/1.31 % (1294844)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2571517964:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/1.31 % (1294847)Also succeeded, but the first one will report.
% 2.53/1.31 % (1294844)Instruction limit reached!
% 2.53/1.31 % (1294844)------------------------------
% 2.53/1.31 % (1294844)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1294844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1294844)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1294844)Termination reason: Instruction limit
% 2.53/1.31 % (1294844)Termination phase: Saturation
% 2.53/1.31 % (1294844)Time elapsed: 0.068 s
% 2.53/1.31 % (1294844)Peak memory usage: 90 MB
% 2.53/1.31 % (1294844)Instructions burned: 110 (million)
% 2.53/1.31 % (1294846)Instruction limit reached!
% 2.53/1.31 % (1294846)------------------------------
% 2.53/1.31 % (1294846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1294846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1294846)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1294846)Termination reason: Instruction limit
% 2.53/1.31 % (1294846)Termination phase: Saturation
% 2.53/1.31 % (1294846)Time elapsed: 0.106 s
% 2.53/1.31 % (1294846)Peak memory usage: 90 MB
% 2.53/1.31 % (1294846)Instructions burned: 140 (million)
% 2.53/1.31 % (1294845)Refutation found. Thanks to Tanya!
% 2.53/1.31 % SZS status Theorem for theBenchmark
% 2.53/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/1.31 % (1294845)------------------------------
% 2.53/1.31 % (1294845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.31 % (1294845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.31 % (1294845)CaDiCaL version: 2.1.3
% 2.53/1.31 % (1294845)Termination reason: Refutation
% 2.53/1.31 % (1294845)Time elapsed: 0.007 s
% 2.53/1.31 % (1294845)Peak memory usage: 89 MB
% 2.53/1.31 % (1294845)Instructions burned: 17 (million)
% 2.53/1.31 % (1294845)------------------------------
% 2.53/1.31 % (1294845)------------------------------
% 2.53/1.31 % (1294836)Success in time 0.269 s
% 2.53/1.31 % Vampire exiting
%------------------------------------------------------------------------------