%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM614+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 : n019.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 4.04s 1.54s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 12 unt; 0 def)
% Number of atoms : 133 ( 37 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 171 ( 65 ~; 66 |; 33 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 42 ( 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(f80,axiom,
( aElementOf0(xk,szNzAzT0)
& szszuzczcdt0(xk) = xK ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
fof(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(f108,axiom,
aSubsetOf0(xP,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5208) ).
fof(f109,axiom,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(f110,conjecture,
aElementOf0(xP,slbdtsldtrb0(xO,xk)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f111,negated_conjecture,
~ aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(negated_conjecture,[status(cth)],[f110]) ).
fof(f119,plain,
~ aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(flattening,[],[f111]) ).
fof(f194,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(f195,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,[],[f194]) ).
fof(f290,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,[],[f195]) ).
fof(f291,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,[],[f290]) ).
fof(f292,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,[],[f291]) ).
fof(f293,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = slbdtsldtrb0(X0,X1)
| ~ aSet0(X2)
| ( ( ~ aSubsetOf0(sK14(X0,X1,X2),X0)
| sbrdtbr0(sK14(X0,X1,X2)) != X1
| ~ aElementOf0(sK14(X0,X1,X2),X2) )
& ( ( aSubsetOf0(sK14(X0,X1,X2),X0)
& sbrdtbr0(sK14(X0,X1,X2)) = X1 )
| aElementOf0(sK14(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,[sK14]),skolemize(X3,sK14(X0,X1,X2))],[f292]) ).
fof(f414,plain,
! [X2,X0,X1,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| sbrdtbr0(X4) != X1
| slbdtsldtrb0(X0,X1) != X2
| ~ aSet0(X0)
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f470,plain,
aElementOf0(xk,szNzAzT0),
inference(cnf_transformation,[],[f80]) ).
fof(f504,plain,
aSet0(xO),
inference(cnf_transformation,[],[f95]) ).
fof(f522,plain,
aSubsetOf0(xP,xO),
inference(cnf_transformation,[],[f108]) ).
fof(f523,plain,
xk = sbrdtbr0(xP),
inference(cnf_transformation,[],[f109]) ).
fof(f524,plain,
~ aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(cnf_transformation,[],[f119]) ).
fof(f543,plain,
! [X2,X0,X4] :
( aElementOf0(X4,X2)
| ~ aSubsetOf0(X4,X0)
| slbdtsldtrb0(X0,sbrdtbr0(X4)) != X2
| ~ aSet0(X0)
| ~ aElementOf0(sbrdtbr0(X4),szNzAzT0) ),
inference(equality_resolution,[],[f414]) ).
fof(f544,plain,
! [X0,X4] :
( ~ aElementOf0(sbrdtbr0(X4),szNzAzT0)
| ~ aSubsetOf0(X4,X0)
| ~ aSet0(X0)
| aElementOf0(X4,slbdtsldtrb0(X0,sbrdtbr0(X4))) ),
inference(equality_resolution,[],[f543]) ).
fof(f1079,plain,
! [X0] :
( ~ aElementOf0(xk,szNzAzT0)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk)) ),
inference(superposition,[],[f544,f523]) ).
fof(f1084,plain,
! [X0] :
( ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| aElementOf0(xP,slbdtsldtrb0(X0,xk)) ),
inference(forward_subsumption_resolution,[],[f1079,f470]) ).
fof(f2625,plain,
( ~ aSet0(xO)
| aElementOf0(xP,slbdtsldtrb0(xO,xk)) ),
inference(resolution,[],[f1084,f522]) ).
fof(f2645,plain,
aElementOf0(xP,slbdtsldtrb0(xO,xk)),
inference(forward_subsumption_resolution,[],[f2625,f504]) ).
fof(f2646,plain,
$false,
inference(forward_subsumption_resolution,[],[f2645,f524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM614+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n019.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 20:45:49 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.04/1.54 % (3389010)Detected formulas, will run a generic FOF schedule.
% 4.04/1.54 % (3389017)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=3031872566:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.04/1.54 % (3389020)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=155956631:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.04/1.54 % (3389021)dis-21_1_sil=8000:lcm=predicate:random_seed=1752678896: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)
% 4.04/1.54 % (3389015)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=2942181851:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.04/1.54 % (3389016)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=3914764475:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.04/1.54 % (3389019)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2257843967:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.04/1.54 % (3389018)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3603049595:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.04/1.54 % (3389018)Instruction limit reached!
% 4.04/1.54 % (3389018)------------------------------
% 4.04/1.54 % (3389018)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.54 % (3389018)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.54 % (3389018)CaDiCaL version: 2.1.3
% 4.04/1.54 % (3389018)Termination reason: Instruction limit
% 4.04/1.54 % (3389018)Termination phase: Saturation
% 4.04/1.54 % (3389018)Time elapsed: 0.065 s
% 4.04/1.54 % (3389018)Peak memory usage: 89 MB
% 4.04/1.54 % (3389018)Instructions burned: 110 (million)
% 4.04/1.54 % (3389019)Instruction limit reached!
% 4.04/1.54 % (3389019)------------------------------
% 4.04/1.54 % (3389019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.54 % (3389019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.54 % (3389019)CaDiCaL version: 2.1.3
% 4.04/1.54 % (3389019)Termination reason: Instruction limit
% 4.04/1.54 % (3389019)Termination phase: Saturation
% 4.04/1.54 % (3389019)Time elapsed: 0.068 s
% 4.04/1.54 % (3389019)Peak memory usage: 88 MB
% 4.04/1.54 % (3389019)Instructions burned: 120 (million)
% 4.04/1.54 % (3389021)Instruction limit reached!
% 4.04/1.54 % (3389021)------------------------------
% 4.04/1.54 % (3389021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.54 % (3389021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.54 % (3389021)CaDiCaL version: 2.1.3
% 4.04/1.54 % (3389021)Termination reason: Instruction limit
% 4.04/1.54 % (3389021)Termination phase: Saturation
% 4.04/1.54 % (3389021)Time elapsed: 0.072 s
% 4.04/1.54 % (3389021)Peak memory usage: 91 MB
% 4.04/1.54 % (3389021)Instructions burned: 129 (million)
% 4.04/1.54 % (3389020)First to succeed.
% 4.04/1.54 % (3389020)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3389010"
% 4.04/1.54 % (3389031)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2769356010:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.04/1.54 % (3389030)lrs+10_1_sil=32000:urr=on:br=off:random_seed=596905378:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.04/1.54 % (3389029)lrs+10_1_sil=8000:sp=occurrence:random_seed=1270992381:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.04/1.54 % (3389030)Refutation not found, incomplete strategy
% 4.04/1.54 % (3389030)------------------------------
% 4.04/1.54 % (3389030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.54 % (3389030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.54 % (3389030)CaDiCaL version: 2.1.3
% 4.04/1.54 % (3389030)Termination reason: Refutation not found, incomplete strategy
% 4.04/1.54 % (3389030)Time elapsed: 0.002 s
% 4.04/1.54 % (3389030)Peak memory usage: 88 MB
% 4.04/1.54 % (3389030)Instructions burned: 2 (million)
% 4.04/1.54 % (3389031)Also succeeded, but the first one will report.
% 4.04/1.54 % (3389020)Refutation found. Thanks to Tanya!
% 4.04/1.54 % SZS status Theorem for theBenchmark
% 4.04/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 4.04/1.54 % (3389020)------------------------------
% 4.04/1.54 % (3389020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.04/1.54 % (3389020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.04/1.54 % (3389020)CaDiCaL version: 2.1.3
% 4.04/1.54 % (3389020)Termination reason: Refutation
% 4.04/1.54 % (3389020)Time elapsed: 0.092 s
% 4.04/1.54 % (3389020)Peak memory usage: 90 MB
% 4.04/1.54 % (3389020)Instructions burned: 122 (million)
% 4.04/1.54 % (3389020)------------------------------
% 4.04/1.54 % (3389020)------------------------------
% 4.04/1.54 % (3389010)Success in time 0.489 s
% 4.04/1.54 % Vampire exiting
%------------------------------------------------------------------------------