%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM610+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 : n013.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 12:15:58 PM UTC 2026
% Result : Theorem 3.60s 1.47s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 113 ( 3 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 147 ( 69 ~; 57 |; 17 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 36 !; 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(f95,axiom,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
fof(f100,axiom,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5093) ).
fof(f104,axiom,
( aSet0(xP)
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
fof(f107,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5195) ).
fof(f108,conjecture,
aSubsetOf0(xP,xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f109,negated_conjecture,
~ aSubsetOf0(xP,xO),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f117,plain,
~ aSubsetOf0(xP,xO),
inference(flattening,[],[f109]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f251,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,[],[f124]) ).
fof(f252,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,[],[f251]) ).
fof(f253,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,[],[f252]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK5(X0,X1),X0)
& aElementOf0(sK5(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f253]) ).
fof(f317,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f254]) ).
fof(f318,plain,
! [X0,X1] :
( aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f254]) ).
fof(f319,plain,
! [X0,X1] :
( aElementOf0(sK5(X0,X1),X1)
| ~ aSet0(X1)
| aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f254]) ).
fof(f320,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK5(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f254]) ).
fof(f502,plain,
aSet0(xO),
inference(cnf_transformation,[],[f95]) ).
fof(f511,plain,
aSubsetOf0(xQ,xO),
inference(cnf_transformation,[],[f100]) ).
fof(f516,plain,
aSet0(xP),
inference(cnf_transformation,[],[f104]) ).
fof(f519,plain,
aSubsetOf0(xP,xQ),
inference(cnf_transformation,[],[f107]) ).
fof(f520,plain,
~ aSubsetOf0(xP,xO),
inference(cnf_transformation,[],[f117]) ).
fof(f621,plain,
( ~ aSet0(xP)
| ~ aElementOf0(sK5(xO,xP),xO)
| ~ aSet0(xO) ),
inference(resolution,[],[f320,f520]) ).
fof(f622,plain,
( ~ aElementOf0(sK5(xO,xP),xO)
| ~ aSet0(xO) ),
inference(forward_subsumption_resolution,[],[f621,f516]) ).
fof(f623,plain,
~ aElementOf0(sK5(xO,xP),xO),
inference(forward_subsumption_resolution,[],[f622,f502]) ).
fof(f624,plain,
! [X0] :
( ~ aElementOf0(sK5(xO,xP),X0)
| ~ aSubsetOf0(X0,xO)
| ~ aSet0(xO) ),
inference(resolution,[],[f623,f317]) ).
fof(f625,plain,
! [X0] :
( ~ aElementOf0(sK5(xO,xP),X0)
| ~ aSubsetOf0(X0,xO) ),
inference(forward_subsumption_resolution,[],[f624,f502]) ).
fof(f631,plain,
! [X0,X1] :
( ~ aElementOf0(sK5(xO,xP),X1)
| ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(resolution,[],[f625,f317]) ).
fof(f633,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(X0)
| ~ aSet0(xP)
| aSubsetOf0(xP,xO)
| ~ aSet0(xO) ),
inference(resolution,[],[f631,f319]) ).
fof(f636,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xP)
| aSubsetOf0(xP,xO)
| ~ aSet0(xO) ),
inference(forward_subsumption_resolution,[],[f633,f318]) ).
fof(f637,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| aSubsetOf0(xP,xO)
| ~ aSet0(xO) ),
inference(forward_subsumption_resolution,[],[f636,f516]) ).
fof(f638,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0)
| ~ aSet0(xO) ),
inference(forward_subsumption_resolution,[],[f637,f520]) ).
fof(f639,plain,
! [X0] :
( ~ aSubsetOf0(X0,xO)
| ~ aSubsetOf0(xP,X0) ),
inference(forward_subsumption_resolution,[],[f638,f502]) ).
fof(f644,plain,
~ aSubsetOf0(xP,xQ),
inference(resolution,[],[f639,f511]) ).
fof(f645,plain,
$false,
inference(forward_subsumption_resolution,[],[f644,f519]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM610+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.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 20:44:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.60/1.47 % (532096)Detected formulas, will run a generic FOF schedule.
% 3.60/1.47 % (532104)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=941598601:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.47 % (532104)Instruction limit reached!
% 3.60/1.47 % (532104)------------------------------
% 3.60/1.47 % (532104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.47 % (532104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.47 % (532104)CaDiCaL version: 2.1.3
% 3.60/1.47 % (532104)Termination reason: Instruction limit
% 3.60/1.47 % (532104)Termination phase: Saturation
% 3.60/1.47 % (532104)Time elapsed: 0.037 s
% 3.60/1.47 % (532104)Peak memory usage: 90 MB
% 3.60/1.47 % (532104)Instructions burned: 110 (million)
% 3.60/1.47 % (532105)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2688413561:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.47 % (532106)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=629933697:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.47 % (532102)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=1358770824:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.47 % (532103)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=2926921506:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.47 % (532101)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=2723460046:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.47 % (532107)dis-21_1_sil=8000:lcm=predicate:random_seed=2952468518: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)
% 3.60/1.47 % (532106)First to succeed.
% 3.60/1.47 % (532106)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-532096"
% 3.60/1.47 % (532107)Also succeeded, but the first one will report.
% 3.60/1.47 % (532105)Also succeeded, but the first one will report.
% 3.60/1.47 % (532109)lrs+10_1_sil=8000:sp=occurrence:random_seed=3412003370:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.60/1.47 % (532109)Also succeeded, but the first one will report.
% 3.60/1.47 % (532106)Refutation found. Thanks to Tanya!
% 3.60/1.47 % SZS status Theorem for theBenchmark
% 3.60/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.47 % (532106)------------------------------
% 3.60/1.47 % (532106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.47 % (532106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.47 % (532106)CaDiCaL version: 2.1.3
% 3.60/1.47 % (532106)Termination reason: Refutation
% 3.60/1.47 % (532106)Time elapsed: 0.011 s
% 3.60/1.47 % (532106)Peak memory usage: 89 MB
% 3.60/1.47 % (532106)Instructions burned: 15 (million)
% 3.60/1.47 % (532106)------------------------------
% 3.60/1.47 % (532106)------------------------------
% 3.60/1.47 % (532096)Success in time 0.434 s
% 3.60/1.47 % Vampire exiting
%------------------------------------------------------------------------------