%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU110+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 : n011.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 12:47:16 PM UTC 2026
% Result : Theorem 6.46s 1.97s
% Output : Refutation 6.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 11 unt; 0 def)
% Number of atoms : 152 ( 13 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 187 ( 73 ~; 72 |; 31 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 77 ( 70 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f9,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X1,X2) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f27,conjecture,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f40,plain,
? [X0,X1] :
( ~ subset(finite_subsets(X0),finite_subsets(X1))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f41,plain,
! [X0,X1] :
( ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f43,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ subset(X1,X2) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f46,plain,
( ~ subset(finite_subsets(sK0),finite_subsets(sK1))
& subset(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f41]) ).
fof(f48,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ( ( ~ subset(sK2(X0,X1),X0)
| ~ finite(sK2(X0,X1))
| ~ in(sK2(X0,X1),X1) )
& ( ( subset(sK2(X0,X1),X0)
& finite(sK2(X0,X1)) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f49]) ).
fof(f52,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,[],[f45]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK3(X0,X1),X1)
& in(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f53]) ).
fof(f55,plain,
subset(sK0,sK1),
inference(cnf_transformation,[],[f46]) ).
fof(f56,plain,
~ subset(finite_subsets(sK0),finite_subsets(sK1)),
inference(cnf_transformation,[],[f46]) ).
fof(f58,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f59,plain,
! [X3,X0,X1] :
( finite(X3)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f60,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f61,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f68,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0,X1] :
( in(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f72,plain,
! [X0,X1] :
( ~ in(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f73,plain,
! [X3,X0] :
( in(X3,finite_subsets(X0))
| ~ subset(X3,X0)
| ~ finite(X3)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f61]) ).
fof(f74,plain,
! [X3,X0] :
( ~ in(X3,finite_subsets(X0))
| subset(X3,X0)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f60]) ).
fof(f75,plain,
! [X3,X0] :
( ~ in(X3,finite_subsets(X0))
| finite(X3)
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f59]) ).
fof(f81,plain,
in(sK3(finite_subsets(sK0),finite_subsets(sK1)),finite_subsets(sK0)),
inference(unit_resulting_resolution,[],[f71,f56]) ).
fof(f82,plain,
~ in(sK3(finite_subsets(sK0),finite_subsets(sK1)),finite_subsets(sK1)),
inference(unit_resulting_resolution,[],[f72,f56]) ).
fof(f92,plain,
finite(sK3(finite_subsets(sK0),finite_subsets(sK1))),
inference(unit_resulting_resolution,[],[f75,f58,f81]) ).
fof(f94,plain,
subset(sK3(finite_subsets(sK0),finite_subsets(sK1)),sK0),
inference(unit_resulting_resolution,[],[f74,f58,f81]) ).
fof(f97,plain,
~ subset(sK3(finite_subsets(sK0),finite_subsets(sK1)),sK1),
inference(unit_resulting_resolution,[],[f73,f58,f82,f92]) ).
fof(f99,plain,
subset(sK3(finite_subsets(sK0),finite_subsets(sK1)),sK1),
inference(unit_resulting_resolution,[],[f68,f55,f94]) ).
fof(f103,plain,
$false,
inference(forward_subsumption_resolution,[],[f99,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n011.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:35:36 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 6.46/1.97 % (2991275)Detected formulas, will run a generic FOF schedule.
% 6.46/1.97 % (2991297)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=1347567823:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.46/1.97 % (2991300)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2228862261:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.46/1.97 % (2991298)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=1311735894:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.46/1.97 % (2991301)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1124764123:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.46/1.97 % (2991299)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1854324181:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.46/1.97 % (2991296)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=3439641914:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.46/1.97 % (2991299)Refutation not found, incomplete strategy
% 6.46/1.97 % (2991299)------------------------------
% 6.46/1.97 % (2991299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991299)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991299)Termination reason: Refutation not found, incomplete strategy
% 6.46/1.97 % (2991299)Time elapsed: 0.002 s
% 6.46/1.97 % (2991299)Peak memory usage: 88 MB
% 6.46/1.97 % (2991302)dis-21_1_sil=8000:lcm=predicate:random_seed=943995740: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)
% 6.46/1.97 % (2991300)Instruction limit reached!
% 6.46/1.97 % (2991300)------------------------------
% 6.46/1.97 % (2991300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991300)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991300)Termination reason: Instruction limit
% 6.46/1.97 % (2991300)Termination phase: Saturation
% 6.46/1.97 % (2991300)Time elapsed: 0.077 s
% 6.46/1.97 % (2991300)Peak memory usage: 88 MB
% 6.46/1.97 % (2991300)Instructions burned: 119 (million)
% 6.46/1.97 % (2991301)Instruction limit reached!
% 6.46/1.97 % (2991301)------------------------------
% 6.46/1.97 % (2991301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991301)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991301)Termination reason: Instruction limit
% 6.46/1.97 % (2991301)Termination phase: Saturation
% 6.46/1.97 % (2991301)Time elapsed: 0.075 s
% 6.46/1.97 % (2991301)Peak memory usage: 88 MB
% 6.46/1.97 % (2991301)Instructions burned: 139 (million)
% 6.46/1.97 % (2991302)Instruction limit reached!
% 6.46/1.97 % (2991302)------------------------------
% 6.46/1.97 % (2991302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991302)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991302)Termination reason: Instruction limit
% 6.46/1.97 % (2991302)Termination phase: Saturation
% 6.46/1.97 % (2991302)Time elapsed: 0.105 s
% 6.46/1.97 % (2991302)Peak memory usage: 90 MB
% 6.46/1.97 % (2991302)Instructions burned: 129 (million)
% 6.46/1.97 % (2991315)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2119023718:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.46/1.97 % (2991315)First to succeed.
% 6.46/1.97 % (2991315)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2991275"
% 6.46/1.97 % (2991314)lrs+10_1_sil=8000:sp=occurrence:random_seed=779913189:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.46/1.97 % (2991314)Also succeeded, but the first one will report.
% 6.46/1.97 % (2991318)lrs+1011_1_sil=32000:sp=occurrence:random_seed=996062661:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 6.46/1.97 % (2991299)------------------------------
% 6.46/1.97 % (2991299)------------------------------
% 6.46/1.97 % (2991318)Instruction limit reached!
% 6.46/1.97 % (2991318)------------------------------
% 6.46/1.97 % (2991318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991318)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991318)Termination reason: Instruction limit
% 6.46/1.97 % (2991318)Termination phase: Saturation
% 6.46/1.97 % (2991318)Time elapsed: 0.165 s
% 6.46/1.97 % (2991318)Peak memory usage: 88 MB
% 6.46/1.97 % (2991318)Instructions burned: 326 (million)
% 6.46/1.97 % (2991297)Also succeeded, but the first one will report.
% 6.46/1.97 % (2991325)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3277251083:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 6.46/1.97 % (2991325)Also succeeded, but the first one will report.
% 6.46/1.97 % (2991315)Refutation found. Thanks to Tanya!
% 6.46/1.97 % SZS status Theorem for theBenchmark
% 6.46/1.97 % SZS output start Proof for theBenchmark
% See solution above
% 6.46/1.97 % (2991315)------------------------------
% 6.46/1.97 % (2991315)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.46/1.97 % (2991315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.46/1.97 % (2991315)CaDiCaL version: 2.1.3
% 6.46/1.97 % (2991315)Termination reason: Refutation
% 6.46/1.97 % (2991315)Time elapsed: 0.004 s
% 6.46/1.97 % (2991315)Peak memory usage: 89 MB
% 6.46/1.97 % (2991315)Instructions burned: 3 (million)
% 6.46/1.97 % (2991315)------------------------------
% 6.46/1.97 % (2991315)------------------------------
% 6.46/1.97 % (2991275)Success in time 0.813 s
% 6.46/1.97 % Vampire exiting
%------------------------------------------------------------------------------