%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 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 12:42:16 PM UTC 2026
% Result : Theorem 2.72s 1.37s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 149 ( 109 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 62 ~; 75 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 42 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ~ ( X0 != empty_set
& X0 != singleton(X1)
& X0 != singleton(X2)
& X0 != unordered_pair(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l46_zfmisc_1) ).
fof(f9,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f2]) ).
fof(f10,plain,
? [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<~> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f11,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
<=> ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f12,plain,
? [X0,X1,X2] :
( ( ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 )
| ~ subset(X0,unordered_pair(X1,X2)) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f13,plain,
? [X0,X1,X2] :
( ( ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 )
| ~ subset(X0,unordered_pair(X1,X2)) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
( ( ( empty_set != sK0
& sK0 != singleton(sK1)
& sK0 != singleton(sK2)
& sK0 != unordered_pair(sK1,sK2) )
| ~ subset(sK0,unordered_pair(sK1,sK2)) )
& ( empty_set = sK0
| sK0 = singleton(sK1)
| sK0 = singleton(sK2)
| sK0 = unordered_pair(sK1,sK2)
| subset(sK0,unordered_pair(sK1,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( subset(X0,unordered_pair(X1,X2))
| ( empty_set != X0
& singleton(X1) != X0
& singleton(X2) != X0
& unordered_pair(X1,X2) != X0 ) )
& ( empty_set = X0
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| ~ subset(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f15]) ).
fof(f19,plain,
( subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| sK0 = singleton(sK2)
| sK0 = unordered_pair(sK1,sK2)
| empty_set = sK0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
( sK0 != unordered_pair(sK1,sK2)
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( sK0 != singleton(sK2)
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
( sK0 != singleton(sK1)
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
( empty_set != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ subset(X0,unordered_pair(X1,X2))
| singleton(X1) = X0
| singleton(X2) = X0
| unordered_pair(X1,X2) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X2) != X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| singleton(X1) != X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0,X1] :
( subset(X0,unordered_pair(X1,X2))
| empty_set != X0 ),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
! [X2,X1] : subset(empty_set,unordered_pair(X1,X2)),
inference(equality_resolution,[],[f31]) ).
fof(f35,plain,
! [X2,X1] : subset(singleton(X1),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f30]) ).
fof(f36,plain,
! [X2,X1] : subset(singleton(X2),unordered_pair(X1,X2)),
inference(equality_resolution,[],[f29]) ).
fof(f48,plain,
( sK0 = singleton(sK1)
| sK0 = singleton(sK2)
| sK0 = unordered_pair(sK1,sK2)
| empty_set = sK0
| sK0 = singleton(sK1)
| sK0 = singleton(sK2)
| sK0 = unordered_pair(sK1,sK2)
| empty_set = sK0 ),
inference(resolution,[],[f27,f19]) ).
fof(f51,plain,
( sK0 = unordered_pair(sK1,sK2)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(duplicate_literal_removal,[],[f48]) ).
fof(f52,plain,
( sK0 != sK0
| ~ subset(sK0,sK0)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f20,f51]) ).
fof(f57,plain,
( ~ subset(sK0,sK0)
| sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f52]) ).
fof(f58,plain,
( sK0 = singleton(sK2)
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(forward_subsumption_resolution,[],[f57,f25]) ).
fof(f59,plain,
( sK0 != sK0
| ~ subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f21,f58]) ).
fof(f60,plain,
! [X0] :
( subset(sK0,unordered_pair(X0,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(superposition,[],[f36,f58]) ).
fof(f62,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(trivial_inequality_removal,[],[f59]) ).
fof(f63,plain,
( ~ subset(sK0,unordered_pair(sK1,sK2))
| empty_set = sK0 ),
inference(forward_subsumption_resolution,[],[f62,f22]) ).
fof(f64,plain,
~ subset(sK0,unordered_pair(sK1,sK2)),
inference(forward_subsumption_resolution,[],[f63,f23]) ).
fof(f67,plain,
( sK0 = singleton(sK1)
| empty_set = sK0 ),
inference(resolution,[],[f60,f64]) ).
fof(f76,plain,
! [X0] :
( subset(sK0,unordered_pair(sK1,X0))
| empty_set = sK0 ),
inference(superposition,[],[f35,f67]) ).
fof(f82,plain,
empty_set = sK0,
inference(resolution,[],[f76,f64]) ).
fof(f90,plain,
~ subset(empty_set,unordered_pair(sK1,sK2)),
inference(superposition,[],[f64,f82]) ).
fof(f92,plain,
$false,
inference(forward_subsumption_resolution,[],[f90,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET901+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n004.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:07:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.72/1.37 % (4113700)Detected formulas, will run a generic FOF schedule.
% 2.72/1.37 % (4113794)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1646818713:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.37 % (4113794)First to succeed.
% 2.72/1.37 % (4113794)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4113700"
% 2.72/1.37 % (4113787)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=1019864191:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.72/1.37 % (4113782)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=3817930747:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.72/1.37 % (4113792)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=507042317:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.72/1.37 % (4113796)dis-21_1_sil=8000:lcm=predicate:random_seed=1819577454: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)
% 2.72/1.37 % (4113796)Refutation not found, incomplete strategy
% 2.72/1.37 % (4113796)------------------------------
% 2.72/1.37 % (4113796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.37 % (4113796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.37 % (4113796)CaDiCaL version: 2.1.3
% 2.72/1.37 % (4113796)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.37 % (4113796)Time elapsed: 0.002 s
% 2.72/1.37 % (4113796)Peak memory usage: 88 MB
% 2.72/1.37 % (4113796)Instructions burned: 1 (million)
% 2.72/1.37 % (4113795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4168463213:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.72/1.37 % (4113795)Also succeeded, but the first one will report.
% 2.72/1.37 % (4113793)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2855670914:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.72/1.37 % (4113793)Also succeeded, but the first one will report.
% 2.72/1.37 % (4113794)Refutation found. Thanks to Tanya!
% 2.72/1.37 % SZS status Theorem for theBenchmark
% 2.72/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.37 % (4113794)------------------------------
% 2.72/1.37 % (4113794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.37 % (4113794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.37 % (4113794)CaDiCaL version: 2.1.3
% 2.72/1.37 % (4113794)Termination reason: Refutation
% 2.72/1.37 % (4113794)Time elapsed: 0.002 s
% 2.72/1.37 % (4113794)Peak memory usage: 88 MB
% 2.72/1.37 % (4113794)Instructions burned: 4 (million)
% 2.72/1.37 % (4113794)------------------------------
% 2.72/1.37 % (4113794)------------------------------
% 2.72/1.37 % (4113700)Success in time 0.312 s
% 2.72/1.37 % Vampire exiting
%------------------------------------------------------------------------------