%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU435+3 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:49:02 PM UTC 2026
% Result : Theorem 0.30s 2.50s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 30 ( 13 ~; 7 |; 5 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-6 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19053,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
fof(f19109,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_2) ).
fof(f19110,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
inference(negated_conjecture,[status(cth)],[f19109]) ).
fof(f19115,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ~ m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(ennf_transformation,[],[f19110]) ).
fof(f19132,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(ennf_transformation,[],[f19053]) ).
fof(f19133,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(flattening,[],[f19132]) ).
fof(f19136,plain,
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
& m1_subset_1(sK5,k1_zfmisc_1(sK3))
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f19115]) ).
fof(f19143,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))),
inference(cnf_transformation,[],[f19136]) ).
fof(f19144,plain,
m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(cnf_transformation,[],[f19136]) ).
fof(f19145,plain,
~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4))),
inference(cnf_transformation,[],[f19136]) ).
fof(f19167,plain,
! [X2,X3,X0,X1,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3)) ),
inference(cnf_transformation,[],[f19133]) ).
fof(f19205,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))))
| ~ m1_subset_1(sK5,k1_zfmisc_1(sK3)) ),
inference(resolution,[],[f19167,f19145]) ).
fof(f19206,plain,
~ m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(forward_subsumption_resolution,[],[f19205,f19143]) ).
fof(f19207,plain,
$false,
inference(forward_subsumption_resolution,[],[f19206,f19144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU435+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 % Computer : n004.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Mon Sep 28 05:27:25 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.54 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
% 0.30/2.50 % (28051)Detected formulas, will run a generic FOF schedule.
% 0.30/2.50 % (28178)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=3856054976:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2995 on theBenchmark for (2995ds/134677Mi)
% 0.30/2.50 % (28184)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1856472200:s2a=on:i=139:gtg=position_2995 on theBenchmark for (2995ds/139Mi)
% 0.30/2.50 % (28180)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=1355753141:i=141695:sd=1:nm=32:gsp=on:ss=included_2995 on theBenchmark for (2995ds/141695Mi)
% 0.30/2.50 % (28186)dis-21_1_sil=8000:lcm=predicate:random_seed=4223467463:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2995 on theBenchmark for (2995ds/129Mi)
% 0.30/2.50 % (28181)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=126908628:i=109:sd=1:ins=1:gsp=on:ss=axioms_2995 on theBenchmark for (2995ds/109Mi)
% 0.30/2.50 % (28176)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=1292226744:i=141193_2995 on theBenchmark for (2995ds/141193Mi)
% 0.30/2.50 % (28183)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3508000911:i=119:av=off:ss=axioms_2995 on theBenchmark for (2995ds/119Mi)
% 0.30/2.50 % (28184)Instruction limit reached!
% 0.30/2.50 % (28184)------------------------------
% 0.30/2.50 % (28184)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28184)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28184)Termination reason: Instruction limit
% 0.30/2.50 % (28184)Termination phase: Property scanning
% 0.30/2.50 % (28184)Time elapsed: 0.060 s
% 0.30/2.50 % (28184)Peak memory usage: 112 MB
% 0.30/2.50 % (28184)Instructions burned: 140 (million)
% 0.30/2.50 % (28181)Instruction limit reached!
% 0.30/2.50 % (28181)------------------------------
% 0.30/2.50 % (28181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28181)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28181)Termination reason: Instruction limit
% 0.30/2.50 % (28181)Termination phase: SInE selection
% 0.30/2.50 % (28181)Time elapsed: 0.081 s
% 0.30/2.50 % (28181)Peak memory usage: 112 MB
% 0.30/2.50 % (28181)Instructions burned: 109 (million)
% 0.30/2.50 % (28186)Instruction limit reached!
% 0.30/2.50 % (28186)------------------------------
% 0.30/2.50 % (28186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28186)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28186)Termination reason: Instruction limit
% 0.30/2.50 % (28186)Termination phase: SInE selection
% 0.30/2.50 % (28186)Time elapsed: 0.084 s
% 0.30/2.50 % (28186)Peak memory usage: 113 MB
% 0.30/2.50 % (28186)Instructions burned: 130 (million)
% 0.30/2.50 % (28183)Instruction limit reached!
% 0.30/2.50 % (28183)------------------------------
% 0.30/2.50 % (28183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28183)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28183)Termination reason: Instruction limit
% 0.30/2.50 % (28183)Termination phase: Preprocessing 1
% 0.30/2.50 % (28183)Time elapsed: 0.097 s
% 0.30/2.50 % (28183)Peak memory usage: 113 MB
% 0.30/2.50 % (28183)Instructions burned: 119 (million)
% 0.30/2.50 % (28223)lrs+10_1_sil=8000:sp=occurrence:random_seed=1139720755:i=285:sd=3:ss=axioms:sgt=8_2992 on theBenchmark for (2992ds/285Mi)
% 0.30/2.50 % (28225)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3345455238:i=325:sd=1:ss=axioms:sgt=32_2992 on theBenchmark for (2992ds/325Mi)
% 0.30/2.50 % (28224)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1589461331:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2992 on theBenchmark for (2992ds/157Mi)
% 0.30/2.50 % (28226)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=670951731:s2a=on:i=248:s2at=1.23:gtg=position_2992 on theBenchmark for (2992ds/248Mi)
% 0.30/2.50 % (28224)Instruction limit reached!
% 0.30/2.50 % (28224)------------------------------
% 0.30/2.50 % (28224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28224)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28224)Termination reason: Instruction limit
% 0.30/2.50 % (28224)Termination phase: Property scanning
% 0.30/2.50 % (28224)Time elapsed: 0.069 s
% 0.30/2.50 % (28224)Peak memory usage: 112 MB
% 0.30/2.50 % (28224)Instructions burned: 159 (million)
% 0.30/2.50 % (28225)First to succeed.
% 0.30/2.50 % (28225)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-28051"
% 0.30/2.50 % (28226)Instruction limit reached!
% 0.30/2.50 % (28226)------------------------------
% 0.30/2.50 % (28226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28226)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28226)Termination reason: Instruction limit
% 0.30/2.50 % (28226)Termination phase: Property scanning
% 0.30/2.50 % (28226)Time elapsed: 0.105 s
% 0.30/2.50 % (28226)Peak memory usage: 112 MB
% 0.30/2.50 % (28226)Instructions burned: 250 (million)
% 0.30/2.50 % (28223)Instruction limit reached!
% 0.30/2.50 % (28223)------------------------------
% 0.30/2.50 % (28223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28223)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28223)Termination reason: Instruction limit
% 0.30/2.50 % (28223)Termination phase: Saturation
% 0.30/2.50 % (28223)Time elapsed: 0.226 s
% 0.30/2.50 % (28223)Peak memory usage: 118 MB
% 0.30/2.50 % (28223)Instructions burned: 286 (million)
% 0.30/2.50 % (28231)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3506508770:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2990 on theBenchmark for (2990ds/294Mi)
% 0.30/2.50 % (28232)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3452494045:i=2350_2990 on theBenchmark for (2990ds/2350Mi)
% 0.30/2.50 % (28225)Refutation found. Thanks to Tanya!
% 0.30/2.50 % SZS status Theorem for theBenchmark
% 0.30/2.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/2.50 % (28225)------------------------------
% 0.30/2.50 % (28225)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/2.50 % (28225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/2.50 % (28225)CaDiCaL version: 2.1.3
% 0.30/2.50 % (28225)Termination reason: Refutation
% 0.30/2.50 % (28225)Time elapsed: 0.111 s
% 0.30/2.50 % (28225)Peak memory usage: 118 MB
% 0.30/2.50 % (28225)Instructions burned: 123 (million)
% 0.30/2.50 % (28225)------------------------------
% 0.30/2.50 % (28225)------------------------------
% 0.30/2.50 % (28051)Success in time 1.249 s
% 0.30/2.50 % Vampire exiting
%------------------------------------------------------------------------------