%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU164+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 12:47:31 PM UTC 2026
% Result : Theorem 2.78s 1.37s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 170 ( 36 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 207 ( 79 ~; 90 |; 31 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 99 ( 87 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X2,X3)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f10,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f12,conjecture,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f13,negated_conjecture,
~ ! [X0] : union(powerset(X0)) = X0,
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f10]) ).
fof(f15,plain,
? [X0] : union(powerset(X0)) != X0,
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
sK0 != union(powerset(sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( X1 = powerset(X0)
| ( ( ~ subset(sK2(X0,X1),X0)
| ~ in(sK2(X0,X1),X1) )
& ( subset(sK2(X0,X1),X0)
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) ) )
& ( ? [X3] :
( in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) ) )
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f26,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X2,X4)
& in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ? [X7] :
( in(X5,X7)
& in(X7,X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( X1 = union(X0)
| ( ( ! [X3] :
( ~ in(sK3(X0,X1),X3)
| ~ in(X3,X0) )
| ~ in(sK3(X0,X1),X1) )
& ( ( in(sK3(X0,X1),sK4(X0,X1))
& in(sK4(X0,X1),X0) )
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X5,X6)
| ~ in(X6,X0) ) )
& ( ( in(X5,sK5(X0,X5))
& in(sK5(X0,X5),X0) )
| ~ in(X5,X1) ) )
| union(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f29]) ).
fof(f31,plain,
sK0 != union(powerset(sK0)),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| union(X0) = X1
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( in(sK3(X0,X1),sK4(X0,X1))
| union(X0) = X1
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X3,X0,X1] :
( ~ in(sK3(X0,X1),X3)
| union(X0) = X1
| ~ in(X3,X0)
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f45,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f14]) ).
fof(f46,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f49,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f35]) ).
fof(f50,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f34]) ).
fof(f116,plain,
! [X0,X1] :
( subset(sK4(powerset(X0),X1),X0)
| in(sK3(powerset(X0),X1),X1)
| union(powerset(X0)) = X1 ),
inference(resolution,[],[f41,f50]) ).
fof(f131,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| union(X0) = X1
| ~ in(X1,X0) ),
inference(factoring,[],[f43]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ in(sK3(X0,X1),X2)
| ~ in(X1,X0)
| union(X0) = X1
| ~ subset(X2,X1) ),
inference(resolution,[],[f131,f46]) ).
fof(f582,plain,
! [X0,X1] :
( ~ in(X0,X1)
| union(X1) = X0
| ~ subset(sK4(X1,X0),X0)
| union(X1) = X0
| in(sK3(X1,X0),X0) ),
inference(resolution,[],[f168,f42]) ).
fof(f589,plain,
! [X0,X1] :
( ~ in(X0,X1)
| union(X1) = X0
| ~ subset(sK4(X1,X0),X0)
| in(sK3(X1,X0),X0) ),
inference(duplicate_literal_removal,[],[f582]) ).
fof(f590,plain,
! [X0,X1] :
( ~ subset(sK4(X1,X0),X0)
| union(X1) = X0
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[],[f589,f131]) ).
fof(f1633,plain,
! [X0] :
( union(powerset(X0)) = X0
| ~ in(X0,powerset(X0))
| in(sK3(powerset(X0),X0),X0)
| union(powerset(X0)) = X0 ),
inference(resolution,[],[f590,f116]) ).
fof(f1638,plain,
! [X0] :
( union(powerset(X0)) = X0
| ~ in(X0,powerset(X0))
| in(sK3(powerset(X0),X0),X0) ),
inference(duplicate_literal_removal,[],[f1633]) ).
fof(f1639,plain,
! [X0] :
( union(powerset(X0)) = X0
| ~ in(X0,powerset(X0)) ),
inference(forward_subsumption_resolution,[],[f1638,f131]) ).
fof(f1739,plain,
( sK0 != sK0
| ~ in(sK0,powerset(sK0)) ),
inference(superposition,[],[f31,f1639]) ).
fof(f1845,plain,
~ in(sK0,powerset(sK0)),
inference(trivial_inequality_removal,[],[f1739]) ).
fof(f1846,plain,
~ subset(sK0,sK0),
inference(resolution,[],[f1845,f49]) ).
fof(f1848,plain,
$false,
inference(forward_subsumption_resolution,[],[f1846,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU164+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.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 : Mon Sep 28 03:49:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.78/1.37 % (4133294)Detected formulas, will run a generic FOF schedule.
% 2.78/1.37 % (4133303)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3657532541:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.78/1.37 % (4133303)First to succeed.
% 2.78/1.37 % (4133303)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4133294"
% 2.78/1.37 % (4133302)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1766617040:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.78/1.37 % (4133300)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=4218677541:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.78/1.37 % (4133301)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=1770184442:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.78/1.37 % (4133299)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=24535262:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.78/1.37 % (4133302)Refutation not found, incomplete strategy
% 2.78/1.37 % (4133302)------------------------------
% 2.78/1.37 % (4133302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (4133302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (4133302)CaDiCaL version: 2.1.3
% 2.78/1.37 % (4133302)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.37 % (4133302)Time elapsed: 0.002 s
% 2.78/1.37 % (4133302)Peak memory usage: 88 MB
% 2.78/1.37 % (4133302)Instructions burned: 1 (million)
% 2.78/1.37 % (4133304)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1856150605:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.78/1.37 % (4133305)dis-21_1_sil=8000:lcm=predicate:random_seed=3887102821: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)
% 2.78/1.37 % (4133305)Also succeeded, but the first one will report.
% 2.78/1.37 % (4133304)Instruction limit reached!
% 2.78/1.37 % (4133304)------------------------------
% 2.78/1.37 % (4133304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (4133304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (4133304)CaDiCaL version: 2.1.3
% 2.78/1.37 % (4133304)Termination reason: Instruction limit
% 2.78/1.37 % (4133304)Termination phase: Saturation
% 2.78/1.37 % (4133304)Time elapsed: 0.095 s
% 2.78/1.37 % (4133304)Peak memory usage: 89 MB
% 2.78/1.37 % (4133304)Instructions burned: 140 (million)
% 2.78/1.37 % (4133303)Refutation found. Thanks to Tanya!
% 2.78/1.37 % SZS status Theorem for theBenchmark
% 2.78/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.37 % (4133303)------------------------------
% 2.78/1.37 % (4133303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.37 % (4133303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.37 % (4133303)CaDiCaL version: 2.1.3
% 2.78/1.37 % (4133303)Termination reason: Refutation
% 2.78/1.37 % (4133303)Time elapsed: 0.028 s
% 2.78/1.37 % (4133303)Peak memory usage: 89 MB
% 2.78/1.37 % (4133303)Instructions burned: 81 (million)
% 2.78/1.37 % (4133303)------------------------------
% 2.78/1.37 % (4133303)------------------------------
% 2.78/1.37 % (4133294)Success in time 0.311 s
% 2.78/1.37 % Vampire exiting
%------------------------------------------------------------------------------