%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:48:30 PM UTC 2026
% Result : Theorem 3.67s 1.46s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 67 ( 25 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 31 ~; 24 |; 8 &)
% ( 4 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 26 ( 20 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( element(X1,X0)
=> ( proper_element(X1,X0)
<=> X1 != union(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f39,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f40,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ( proper_element(X1,powerset(X0))
<=> X1 != X0 ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f44,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f45,plain,
? [X0,X1] :
( ( proper_element(X1,powerset(X0))
<~> X1 != X0 )
& element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( ( proper_element(X1,X0)
<=> X1 != union(X0) )
| ~ element(X1,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f49,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f45]) ).
fof(f50,plain,
? [X0,X1] :
( ( X0 = X1
| ~ proper_element(X1,powerset(X0)) )
& ( X1 != X0
| proper_element(X1,powerset(X0)) )
& element(X1,powerset(X0)) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( ( sK0 = sK1
| ~ proper_element(sK1,powerset(sK0)) )
& ( sK0 != sK1
| proper_element(sK1,powerset(sK0)) )
& element(sK1,powerset(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f50]) ).
fof(f54,plain,
! [X0,X1] :
( ( ( proper_element(X1,X0)
| union(X0) = X1 )
& ( X1 != union(X0)
| ~ proper_element(X1,X0) ) )
| ~ element(X1,X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f57,plain,
element(sK1,powerset(sK0)),
inference(cnf_transformation,[],[f51]) ).
fof(f58,plain,
( sK0 != sK1
| proper_element(sK1,powerset(sK0)) ),
inference(cnf_transformation,[],[f51]) ).
fof(f59,plain,
( ~ proper_element(sK1,powerset(sK0))
| sK0 = sK1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f64,plain,
! [X0,X1] :
( union(X0) != X1
| ~ proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f65,plain,
! [X0,X1] :
( union(X0) = X1
| proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f71,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f44]) ).
fof(f72,plain,
! [X0] :
( ~ proper_element(union(X0),X0)
| ~ element(union(X0),X0) ),
inference(equality_resolution,[],[f64]) ).
fof(f73,plain,
! [X0] :
( ~ proper_element(X0,powerset(X0))
| ~ element(X0,powerset(X0)) ),
inference(superposition,[],[f72,f71]) ).
fof(f74,plain,
! [X0,X1] :
( proper_element(X1,powerset(X0))
| X0 = X1
| ~ element(X1,powerset(X0)) ),
inference(superposition,[],[f65,f71]) ).
fof(f79,plain,
( sK0 = sK1
| ~ element(sK1,powerset(sK0))
| sK0 = sK1 ),
inference(resolution,[],[f74,f59]) ).
fof(f85,plain,
( sK0 = sK1
| ~ element(sK1,powerset(sK0)) ),
inference(duplicate_literal_removal,[],[f79]) ).
fof(f87,plain,
sK0 = sK1,
inference(forward_subsumption_resolution,[],[f85,f57]) ).
fof(f88,plain,
( sK0 != sK0
| proper_element(sK0,powerset(sK0)) ),
inference(superposition,[],[f58,f87]) ).
fof(f89,plain,
element(sK0,powerset(sK0)),
inference(superposition,[],[f57,f87]) ).
fof(f90,plain,
proper_element(sK0,powerset(sK0)),
inference(trivial_inequality_removal,[],[f88]) ).
fof(f91,plain,
~ element(sK0,powerset(sK0)),
inference(resolution,[],[f90,f73]) ).
fof(f92,plain,
$false,
inference(forward_subsumption_resolution,[],[f91,f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 28 04:52:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 3.67/1.46 % (3590593)Detected formulas, will run a generic FOF schedule.
% 3.67/1.46 % (3590604)dis-21_1_sil=8000:lcm=predicate:random_seed=51370932: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)
% 3.67/1.46 % (3590598)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=2132021491:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.46 % (3590599)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=4099957676:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.46 % (3590601)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1183639076:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.46 % (3590600)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=3357844526:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.46 % (3590603)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3960572216:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.46 % (3590602)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3477653829:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.46 % (3590604)Instruction limit reached!
% 3.67/1.46 % (3590604)------------------------------
% 3.67/1.46 % (3590604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.46 % (3590604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.46 % (3590604)CaDiCaL version: 2.1.3
% 3.67/1.46 % (3590604)Termination reason: Instruction limit
% 3.67/1.46 % (3590604)Termination phase: Saturation
% 3.67/1.46 % (3590604)Time elapsed: 0.039 s
% 3.67/1.46 % (3590604)Peak memory usage: 89 MB
% 3.67/1.46 % (3590604)Instructions burned: 129 (million)
% 3.67/1.46 % (3590601)Refutation not found, incomplete strategy
% 3.67/1.46 % (3590601)------------------------------
% 3.67/1.46 % (3590601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.46 % (3590601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.46 % (3590601)CaDiCaL version: 2.1.3
% 3.67/1.46 % (3590601)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.46 % (3590601)Time elapsed: 0.001 s
% 3.67/1.46 % (3590601)Peak memory usage: 88 MB
% 3.67/1.46 % (3590602)First to succeed.
% 3.67/1.46 % (3590602)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3590593"
% 3.67/1.46 % (3590603)Also succeeded, but the first one will report.
% 3.67/1.46 % (3590612)lrs+10_1_sil=8000:sp=occurrence:random_seed=3579333244:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.67/1.46 % (3590612)Also succeeded, but the first one will report.
% 3.67/1.46 % (3590601)------------------------------
% 3.67/1.46 % (3590601)------------------------------
% 3.67/1.46 % (3590602)Refutation found. Thanks to Tanya!
% 3.67/1.46 % SZS status Theorem for theBenchmark
% 3.67/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.46 % (3590602)------------------------------
% 3.67/1.46 % (3590602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.46 % (3590602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.46 % (3590602)CaDiCaL version: 2.1.3
% 3.67/1.46 % (3590602)Termination reason: Refutation
% 3.67/1.46 % (3590602)Time elapsed: 0.003 s
% 3.67/1.46 % (3590602)Peak memory usage: 88 MB
% 3.67/1.46 % (3590602)Instructions burned: 2 (million)
% 3.67/1.46 % (3590602)------------------------------
% 3.67/1.46 % (3590602)------------------------------
% 3.67/1.46 % (3590593)Success in time 0.438 s
% 3.67/1.46 % Vampire exiting
%------------------------------------------------------------------------------