%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU148+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 : n010.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 12:47:25 PM UTC 2026
% Result : Theorem 3.67s 1.52s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 80 ( 49 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 88 ( 34 ~; 34 |; 15 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f6,axiom,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( X0 != X1
& subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f23,plain,
( sK3 != sK4
& subset(singleton(sK3),singleton(sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f25,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0] : singleton(X0) != empty_set,
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
subset(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f23]) ).
fof(f38,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f26]) ).
fof(f40,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f39]) ).
fof(f41,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f25]) ).
fof(f47,plain,
( singleton(sK3) = singleton(sK4)
| empty_set = singleton(sK3) ),
inference(resolution,[],[f31,f37]) ).
fof(f50,plain,
singleton(sK3) = singleton(sK4),
inference(forward_subsumption_resolution,[],[f47,f30]) ).
fof(f55,plain,
in(sK4,singleton(sK3)),
inference(superposition,[],[f40,f50]) ).
fof(f57,plain,
sK3 = sK4,
inference(resolution,[],[f55,f41]) ).
fof(f59,plain,
$false,
inference(forward_subsumption_resolution,[],[f57,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU148+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:45:17 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 3.67/1.52 % (1537788)Detected formulas, will run a generic FOF schedule.
% 3.67/1.52 % (1537795)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=2279267744:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.67/1.52 % (1537794)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=745355349:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.67/1.52 % (1537793)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=2266977500:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.67/1.52 % (1537796)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=523011088:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.67/1.52 % (1537797)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1370135757:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.67/1.52 % (1537799)dis-21_1_sil=8000:lcm=predicate:random_seed=13157203: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)
% 3.67/1.52 % (1537798)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=130802561:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.67/1.52 % (1537797)Refutation not found, incomplete strategy
% 3.67/1.52 % (1537797)------------------------------
% 3.67/1.52 % (1537797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.52 % (1537797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.52 % (1537796)Refutation not found, incomplete strategy
% 3.67/1.52 % (1537796)------------------------------
% 3.67/1.52 % (1537796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.52 % (1537797)CaDiCaL version: 2.1.3
% 3.67/1.52 % (1537797)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.52 % (1537797)Time elapsed: 0.001 s
% 3.67/1.52 % (1537796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.52 % (1537797)Peak memory usage: 88 MB
% 3.67/1.52 % (1537796)CaDiCaL version: 2.1.3
% 3.67/1.52 % (1537796)Termination reason: Refutation not found, incomplete strategy
% 3.67/1.52 % (1537796)Time elapsed: 0.001 s
% 3.67/1.52 % (1537796)Peak memory usage: 88 MB
% 3.67/1.52 % (1537798)First to succeed.
% 3.67/1.52 % (1537798)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1537788"
% 3.67/1.52 % (1537799)Instruction limit reached!
% 3.67/1.52 % (1537799)------------------------------
% 3.67/1.52 % (1537799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.52 % (1537799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.52 % (1537799)CaDiCaL version: 2.1.3
% 3.67/1.52 % (1537799)Termination reason: Instruction limit
% 3.67/1.52 % (1537799)Termination phase: Saturation
% 3.67/1.52 % (1537799)Time elapsed: 0.059 s
% 3.67/1.52 % (1537799)Peak memory usage: 88 MB
% 3.67/1.52 % (1537799)Instructions burned: 130 (million)
% 3.67/1.52 % (1537807)lrs+10_1_sil=8000:sp=occurrence:random_seed=1733328334:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.67/1.52 % (1537807)Also succeeded, but the first one will report.
% 3.67/1.52 % (1537796)------------------------------
% 3.67/1.52 % (1537796)------------------------------
% 3.67/1.52 % (1537797)------------------------------
% 3.67/1.52 % (1537797)------------------------------
% 3.67/1.52 % (1537798)Refutation found. Thanks to Tanya!
% 3.67/1.52 % SZS status Theorem for theBenchmark
% 3.67/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.52 % (1537798)------------------------------
% 3.67/1.52 % (1537798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.52 % (1537798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.52 % (1537798)CaDiCaL version: 2.1.3
% 3.67/1.52 % (1537798)Termination reason: Refutation
% 3.67/1.52 % (1537798)Time elapsed: 0.003 s
% 3.67/1.52 % (1537798)Peak memory usage: 89 MB
% 3.67/1.52 % (1537798)Instructions burned: 2 (million)
% 3.67/1.52 % (1537798)------------------------------
% 3.67/1.52 % (1537798)------------------------------
% 3.67/1.52 % (1537788)Success in time 0.427 s
% 3.67/1.52 % Vampire exiting
%------------------------------------------------------------------------------