%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM548+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 : n016.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 12:15:41 PM UTC 2026
% Result : Theorem 2.77s 1.05s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 44 ( 14 unt; 0 def)
% Number of atoms : 208 ( 38 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 267 ( 103 ~; 102 |; 48 &)
% ( 10 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 72 ( 66 !; 6 ?)
% 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(f41,axiom,
! [X0] :
( aSet0(X0)
=> ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardNum) ).
fof(f57,axiom,
! [X0,X1] :
( ( aSet0(X0)
& aElementOf0(X1,szNzAzT0) )
=> ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(f61,axiom,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(f62,axiom,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(f65,axiom,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(f66,conjecture,
isFinite0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f67,negated_conjecture,
~ isFinite0(xQ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f68,plain,
~ isFinite0(xQ),
inference(flattening,[],[f67]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f97,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( X2 = slbdtsldtrb0(X0,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 ) ) ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f97]) ).
fof(f103,plain,
! [X0] :
( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
<=> isFinite0(X0) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f127,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,[],[f90]) ).
fof(f128,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,[],[f127]) ).
fof(f129,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,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK2(X0,X1),X0)
& aElementOf0(sK2(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(nnf_transformation,[],[f98]) ).
fof(f132,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X3] :
( ( aElementOf0(X3,X2)
| ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1 )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| ~ aElementOf0(X3,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ? [X3] :
( ( ~ aSubsetOf0(X3,X0)
| sbrdtbr0(X3) != X1
| ~ aElementOf0(X3,X2) )
& ( ( aSubsetOf0(X3,X0)
& sbrdtbr0(X3) = X1 )
| aElementOf0(X3,X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK3(X0,X1,X2),X0)
| sbrdtbr0(sK3(X0,X1,X2)) != X1
| ~ aElementOf0(sK3(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK3(X0,X1,X2),X0)
& sbrdtbr0(sK3(X0,X1,X2)) = X1 )
| aElementOf0(sK3(X0,X1,X2),X2) ) ) )
& ( ( aSet0(X2)
& ! [X4] :
( ( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1 )
& ( ( aSubsetOf0(X4,X0)
& sbrdtbr0(X4) = X1 )
| ~ aElementOf0(X4,X2) ) ) )
| slbdtsldtrb0(X0,X1) != X2 ) )
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f133]) ).
fof(f136,plain,
! [X0] :
( ( ( aElementOf0(sbrdtbr0(X0),szNzAzT0)
| ~ isFinite0(X0) )
& ( isFinite0(X0)
| ~ aElementOf0(sbrdtbr0(X0),szNzAzT0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f138,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f61]) ).
fof(f141,plain,
aSet0(xS),
inference(cnf_transformation,[],[f62]) ).
fof(f145,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(cnf_transformation,[],[f65]) ).
fof(f146,plain,
~ isFinite0(xQ),
inference(cnf_transformation,[],[f68]) ).
fof(f165,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| aSet0(X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f171,plain,
! [X2,X0,X1,X4] :
( sbrdtbr0(X4) = X1
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f172,plain,
! [X2,X0,X1,X4] :
( aSubsetOf0(X4,X0)
| ~ aElementOf0(X4,X2)
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X0] :
( ~ aElementOf0(sbrdtbr0(X0),szNzAzT0)
| isFinite0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f202,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f172]) ).
fof(f203,plain,
! [X0,X1,X4] :
( ~ aElementOf0(X4,slbdtsldtrb0(X0,X1))
| sbrdtbr0(X4) = X1
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(equality_resolution,[],[f171]) ).
fof(f278,plain,
( aSubsetOf0(xQ,xS)
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f202,f145]) ).
fof(f283,plain,
( aSubsetOf0(xQ,xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f278,f141]) ).
fof(f285,plain,
aSubsetOf0(xQ,xS),
inference(forward_subsumption_resolution,[],[f283,f138]) ).
fof(f288,plain,
( aSet0(xQ)
| ~ aSet0(xS) ),
inference(resolution,[],[f285,f165]) ).
fof(f289,plain,
aSet0(xQ),
inference(forward_subsumption_resolution,[],[f288,f141]) ).
fof(f341,plain,
( xk = sbrdtbr0(xQ)
| ~ aSet0(xS)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(resolution,[],[f203,f145]) ).
fof(f346,plain,
( xk = sbrdtbr0(xQ)
| ~ aElementOf0(xk,szNzAzT0) ),
inference(forward_subsumption_resolution,[],[f341,f141]) ).
fof(f348,plain,
xk = sbrdtbr0(xQ),
inference(forward_subsumption_resolution,[],[f346,f138]) ).
fof(f353,plain,
( ~ aElementOf0(xk,szNzAzT0)
| isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[],[f181,f348]) ).
fof(f362,plain,
( isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(forward_subsumption_resolution,[],[f353,f138]) ).
fof(f365,plain,
~ aSet0(xQ),
inference(forward_subsumption_resolution,[],[f362,f146]) ).
fof(f366,plain,
$false,
inference(forward_subsumption_resolution,[],[f365,f289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM548+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 20:31:17 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.77/1.05 % (2967214)Detected formulas, will run a generic FOF schedule.
% 2.77/1.05 % (2967224)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3806483977:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.77/1.05 % (2967223)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=519941181:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.77/1.05 % (2967220)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=2859036747:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.77/1.05 % (2967221)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=3841130095:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.77/1.05 % (2967225)dis-21_1_sil=8000:lcm=predicate:random_seed=265592300: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)
% 2.77/1.05 % (2967219)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=414641780:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.77/1.05 % (2967222)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1646544122:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.77/1.05 % (2967223)First to succeed.
% 2.77/1.05 % (2967223)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2967214"
% 2.77/1.05 % (2967224)Also succeeded, but the first one will report.
% 2.77/1.05 % (2967225)Instruction limit reached!
% 2.77/1.05 % (2967225)------------------------------
% 2.77/1.05 % (2967225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.05 % (2967225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.05 % (2967225)CaDiCaL version: 2.1.3
% 2.77/1.05 % (2967225)Termination reason: Instruction limit
% 2.77/1.05 % (2967225)Termination phase: Saturation
% 2.77/1.05 % (2967225)Time elapsed: 0.059 s
% 2.77/1.05 % (2967225)Peak memory usage: 88 MB
% 2.77/1.05 % (2967225)Instructions burned: 129 (million)
% 2.77/1.05 % (2967222)Instruction limit reached!
% 2.77/1.05 % (2967222)------------------------------
% 2.77/1.05 % (2967222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.05 % (2967222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.05 % (2967222)CaDiCaL version: 2.1.3
% 2.77/1.05 % (2967222)Termination reason: Instruction limit
% 2.77/1.05 % (2967222)Termination phase: Saturation
% 2.77/1.05 % (2967222)Time elapsed: 0.066 s
% 2.77/1.05 % (2967222)Peak memory usage: 89 MB
% 2.77/1.05 % (2967222)Instructions burned: 110 (million)
% 2.77/1.05 % (2967233)lrs+10_1_sil=8000:sp=occurrence:random_seed=3064025761:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.77/1.05 % (2967233)Also succeeded, but the first one will report.
% 2.77/1.05 % (2967234)lrs+10_1_sil=32000:urr=on:br=off:random_seed=824386841:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.77/1.05 % (2967234)Refutation not found, incomplete strategy
% 2.77/1.05 % (2967234)------------------------------
% 2.77/1.05 % (2967234)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.05 % (2967234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.05 % (2967234)CaDiCaL version: 2.1.3
% 2.77/1.05 % (2967234)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.05 % (2967234)Time elapsed: 0.001 s
% 2.77/1.05 % (2967234)Peak memory usage: 87 MB
% 2.77/1.05 % (2967223)Refutation found. Thanks to Tanya!
% 2.77/1.05 % SZS status Theorem for theBenchmark
% 2.77/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.25 % (2967223)------------------------------
% 3.47/1.25 % (2967223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.25 % (2967223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.25 % (2967223)CaDiCaL version: 2.1.3
% 3.47/1.25 % (2967223)Termination reason: Refutation
% 3.47/1.25 % (2967223)Time elapsed: 0.007 s
% 3.47/1.25 % (2967223)Peak memory usage: 88 MB
% 3.47/1.25 % (2967223)Instructions burned: 9 (million)
% 3.47/1.25 % (2967223)------------------------------
% 3.47/1.25 % (2967223)------------------------------
% 3.47/1.25 % (2967214)Success in time 0.436 s
% 3.47/1.25 % Vampire exiting
%------------------------------------------------------------------------------