%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU424+3 : TPTP v9.3.1. Released v3.4.0.
% 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 12:48:55 PM UTC 2026
% Result : Theorem 10.72s 3.48s
% Output : Refutation 10.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 21 ~; 12 |; 8 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 28 ( 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19053,axiom,
! [X0,X1,X2,X3] :
( ( ~ v1_xboole_0(X0)
& m1_subset_1(X2,k1_zfmisc_1(X0))
& m2_relset_1(X3,X0,X1) )
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_22__relset_2) ).
fof(f19089,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
fof(f19090,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f19089]) ).
fof(f19092,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f19090]) ).
fof(f19101,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(ennf_transformation,[],[f19053]) ).
fof(f19102,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(flattening,[],[f19101]) ).
fof(f19105,plain,
( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(sK3,sK0,sK1)
& m1_subset_1(sK2,k1_zfmisc_1(sK0))
& ~ v1_xboole_0(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19092]) ).
fof(f19116,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f19105]) ).
fof(f19117,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f19105]) ).
fof(f19118,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f19105]) ).
fof(f19119,plain,
~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f19105]) ).
fof(f19138,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| ~ m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f19102]) ).
fof(f19164,plain,
( v1_xboole_0(sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(resolution,[],[f19138,f19119]) ).
fof(f19165,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f19164,f19116]) ).
fof(f19166,plain,
~ m2_relset_1(sK3,sK0,sK1),
inference(forward_subsumption_resolution,[],[f19165,f19117]) ).
fof(f19167,plain,
$false,
inference(forward_subsumption_resolution,[],[f19166,f19118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU424+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 05:21:19 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.44 Running first-order theorem proving
% 0.13/0.44 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
% 10.72/3.48 % (3062943)Detected formulas, will run a generic FOF schedule.
% 10.72/3.48 % (3063062)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=1147279581:i=141193_2988 on theBenchmark for (2988ds/141193Mi)
% 10.72/3.48 % (3063064)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=3674759849:i=141695:sd=1:nm=32:gsp=on:ss=included_2988 on theBenchmark for (2988ds/141695Mi)
% 10.72/3.48 % (3063067)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=524163493:s2a=on:i=139:gtg=position_2988 on theBenchmark for (2988ds/139Mi)
% 10.72/3.48 % (3063066)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3822055086:i=119:av=off:ss=axioms_2988 on theBenchmark for (2988ds/119Mi)
% 10.72/3.48 % (3063065)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3168771512:i=109:sd=1:ins=1:gsp=on:ss=axioms_2988 on theBenchmark for (2988ds/109Mi)
% 10.72/3.48 % (3063063)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=99526885:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2988 on theBenchmark for (2988ds/134677Mi)
% 10.72/3.48 % (3063068)dis-21_1_sil=8000:lcm=predicate:random_seed=3201494699:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2988 on theBenchmark for (2988ds/129Mi)
% 10.72/3.48 % (3063067)Instruction limit reached!
% 10.72/3.48 % (3063067)------------------------------
% 10.72/3.48 % (3063067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063067)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063067)Termination reason: Instruction limit
% 10.72/3.48 % (3063067)Termination phase: Property scanning
% 10.72/3.48 % (3063067)Time elapsed: 0.116 s
% 10.72/3.48 % (3063067)Peak memory usage: 112 MB
% 10.72/3.48 % (3063067)Instructions burned: 140 (million)
% 10.72/3.48 % (3063065)Instruction limit reached!
% 10.72/3.48 % (3063065)------------------------------
% 10.72/3.48 % (3063065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063065)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063065)Termination reason: Instruction limit
% 10.72/3.48 % (3063065)Termination phase: SInE selection
% 10.72/3.48 % (3063065)Time elapsed: 0.123 s
% 10.72/3.48 % (3063065)Peak memory usage: 112 MB
% 10.72/3.48 % (3063065)Instructions burned: 110 (million)
% 10.72/3.48 % (3063066)Instruction limit reached!
% 10.72/3.48 % (3063066)------------------------------
% 10.72/3.48 % (3063066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063066)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063066)Termination reason: Instruction limit
% 10.72/3.48 % (3063066)Termination phase: Preprocessing 1
% 10.72/3.48 % (3063066)Time elapsed: 0.147 s
% 10.72/3.48 % (3063066)Peak memory usage: 113 MB
% 10.72/3.48 % (3063066)Instructions burned: 119 (million)
% 10.72/3.48 % (3063068)Instruction limit reached!
% 10.72/3.48 % (3063068)------------------------------
% 10.72/3.48 % (3063068)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063068)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063068)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063068)Termination reason: Instruction limit
% 10.72/3.48 % (3063068)Termination phase: SInE selection
% 10.72/3.48 % (3063068)Time elapsed: 0.131 s
% 10.72/3.48 % (3063068)Peak memory usage: 112 MB
% 10.72/3.48 % (3063068)Instructions burned: 130 (million)
% 10.72/3.48 % (3063100)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4178070630:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2985 on theBenchmark for (2985ds/157Mi)
% 10.72/3.48 % (3063099)lrs+10_1_sil=8000:sp=occurrence:random_seed=2355452487:i=285:sd=3:ss=axioms:sgt=8_2985 on theBenchmark for (2985ds/285Mi)
% 10.72/3.48 % (3063103)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=1174850532:s2a=on:i=248:s2at=1.23:gtg=position_2984 on theBenchmark for (2984ds/248Mi)
% 10.72/3.48 % (3063102)lrs+1011_1_sil=32000:sp=occurrence:random_seed=157461791:i=325:sd=1:ss=axioms:sgt=32_2984 on theBenchmark for (2984ds/325Mi)
% 10.72/3.48 % (3063100)Instruction limit reached!
% 10.72/3.48 % (3063100)------------------------------
% 10.72/3.48 % (3063100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063100)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063100)Termination reason: Instruction limit
% 10.72/3.48 % (3063100)Termination phase: Property scanning
% 10.72/3.48 % (3063100)Time elapsed: 0.129 s
% 10.72/3.48 % (3063100)Peak memory usage: 112 MB
% 10.72/3.48 % (3063100)Instructions burned: 157 (million)
% 10.72/3.48 % (3063102)First to succeed.
% 10.72/3.48 % (3063103)Instruction limit reached!
% 10.72/3.48 % (3063103)------------------------------
% 10.72/3.48 % (3063103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063103)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063103)Termination reason: Instruction limit
% 10.72/3.48 % (3063103)Termination phase: Property scanning
% 10.72/3.48 % (3063103)Time elapsed: 0.204 s
% 10.72/3.48 % (3063103)Peak memory usage: 112 MB
% 10.72/3.48 % (3063103)Instructions burned: 249 (million)
% 10.72/3.48 % (3063102)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3062943"
% 10.72/3.48 % (3063099)Instruction limit reached!
% 10.72/3.48 % (3063099)------------------------------
% 10.72/3.48 % (3063099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063099)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063099)Termination reason: Instruction limit
% 10.72/3.48 % (3063099)Termination phase: Saturation
% 10.72/3.48 % (3063099)Time elapsed: 0.340 s
% 10.72/3.48 % (3063099)Peak memory usage: 119 MB
% 10.72/3.48 % (3063099)Instructions burned: 285 (million)
% 10.72/3.48 % (3063110)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=378578756:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2981 on theBenchmark for (2981ds/294Mi)
% 10.72/3.48 % (3063111)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2731754963:i=2350_2980 on theBenchmark for (2980ds/2350Mi)
% 10.72/3.48 % (3063102)Refutation found. Thanks to Tanya!
% 10.72/3.48 % SZS status Theorem for theBenchmark
% 10.72/3.48 % SZS output start Proof for theBenchmark
% See solution above
% 10.72/3.48 % (3063102)------------------------------
% 10.72/3.48 % (3063102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/3.48 % (3063102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/3.48 % (3063102)CaDiCaL version: 2.1.3
% 10.72/3.48 % (3063102)Termination reason: Refutation
% 10.72/3.48 % (3063102)Time elapsed: 0.157 s
% 10.72/3.48 % (3063102)Peak memory usage: 118 MB
% 10.72/3.48 % (3063102)Instructions burned: 121 (million)
% 10.72/3.48 % (3063102)------------------------------
% 10.72/3.48 % (3063102)------------------------------
% 10.72/3.48 % (3062943)Success in time 2.384 s
% 10.72/3.48 % Vampire exiting
%------------------------------------------------------------------------------