%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU429+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 : 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 12:48:58 PM UTC 2026
% Result : Theorem 7.38s 2.96s
% Output : Refutation 7.38s
% 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(k1_zfmisc_1(X0)))
& m2_relset_1(X3,X0,X1) )
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_38__relset_2) ).
fof(f19101,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_relset_2) ).
fof(f19102,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f19101]) ).
fof(f19104,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(X0))) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f19102]) ).
fof(f19112,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(ennf_transformation,[],[f19053]) ).
fof(f19113,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(flattening,[],[f19112]) ).
fof(f19116,plain,
( ~ m1_subset_1(a_4_1_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(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)],[f19104]) ).
fof(f19127,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f19116]) ).
fof(f19128,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f19116]) ).
fof(f19129,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f19116]) ).
fof(f19130,plain,
~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f19116]) ).
fof(f19148,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m2_relset_1(X3,X0,X1) ),
inference(cnf_transformation,[],[f19113]) ).
fof(f19174,plain,
( v1_xboole_0(sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(resolution,[],[f19148,f19130]) ).
fof(f19175,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ m2_relset_1(sK3,sK0,sK1) ),
inference(forward_subsumption_resolution,[],[f19174,f19127]) ).
fof(f19176,plain,
~ m2_relset_1(sK3,sK0,sK1),
inference(forward_subsumption_resolution,[],[f19175,f19128]) ).
fof(f19177,plain,
$false,
inference(forward_subsumption_resolution,[],[f19176,f19129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU429+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 05:23:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 7.38/2.96 % (1593440)Detected formulas, will run a generic FOF schedule.
% 7.38/2.96 % (1593446)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=3227711972:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2989 on theBenchmark for (2989ds/134677Mi)
% 7.38/2.96 % (1593448)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=642152461:i=109:sd=1:ins=1:gsp=on:ss=axioms_2989 on theBenchmark for (2989ds/109Mi)
% 7.38/2.96 % (1593449)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3755776269:i=119:av=off:ss=axioms_2989 on theBenchmark for (2989ds/119Mi)
% 7.38/2.96 % (1593447)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=1088798822:i=141695:sd=1:nm=32:gsp=on:ss=included_2989 on theBenchmark for (2989ds/141695Mi)
% 7.38/2.96 % (1593445)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=4177173494:i=141193_2989 on theBenchmark for (2989ds/141193Mi)
% 7.38/2.96 % (1593451)dis-21_1_sil=8000:lcm=predicate:random_seed=4223781750:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2989 on theBenchmark for (2989ds/129Mi)
% 7.38/2.96 % (1593450)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=550044824:s2a=on:i=139:gtg=position_2989 on theBenchmark for (2989ds/139Mi)
% 7.38/2.96 % (1593450)Instruction limit reached!
% 7.38/2.96 % (1593450)------------------------------
% 7.38/2.96 % (1593450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593450)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593450)Termination reason: Instruction limit
% 7.38/2.96 % (1593450)Termination phase: Property scanning
% 7.38/2.96 % (1593450)Time elapsed: 0.060 s
% 7.38/2.96 % (1593450)Peak memory usage: 112 MB
% 7.38/2.96 % (1593450)Instructions burned: 142 (million)
% 7.38/2.96 % (1593448)Instruction limit reached!
% 7.38/2.96 % (1593448)------------------------------
% 7.38/2.96 % (1593448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593448)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593448)Termination reason: Instruction limit
% 7.38/2.96 % (1593448)Termination phase: SInE selection
% 7.38/2.96 % (1593448)Time elapsed: 0.083 s
% 7.38/2.96 % (1593448)Peak memory usage: 112 MB
% 7.38/2.96 % (1593448)Instructions burned: 109 (million)
% 7.38/2.96 % (1593451)Instruction limit reached!
% 7.38/2.96 % (1593451)------------------------------
% 7.38/2.96 % (1593451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593451)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593451)Termination reason: Instruction limit
% 7.38/2.96 % (1593451)Termination phase: SInE selection
% 7.38/2.96 % (1593451)Time elapsed: 0.090 s
% 7.38/2.96 % (1593451)Peak memory usage: 112 MB
% 7.38/2.96 % (1593451)Instructions burned: 130 (million)
% 7.38/2.96 % (1593449)Instruction limit reached!
% 7.38/2.96 % (1593449)------------------------------
% 7.38/2.96 % (1593449)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593449)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593449)Termination reason: Instruction limit
% 7.38/2.96 % (1593449)Termination phase: Preprocessing 1
% 7.38/2.96 % (1593449)Time elapsed: 0.099 s
% 7.38/2.96 % (1593449)Peak memory usage: 113 MB
% 7.38/2.96 % (1593449)Instructions burned: 120 (million)
% 7.38/2.96 % (1593459)lrs+10_1_sil=8000:sp=occurrence:random_seed=4089900895:i=285:sd=3:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/285Mi)
% 7.38/2.96 % (1593460)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1896897650:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/157Mi)
% 7.38/2.96 % (1593461)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2762898604:i=325:sd=1:ss=axioms:sgt=32_2986 on theBenchmark for (2986ds/325Mi)
% 7.38/2.96 % (1593462)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=678309794:s2a=on:i=248:s2at=1.23:gtg=position_2986 on theBenchmark for (2986ds/248Mi)
% 7.38/2.96 % (1593460)Instruction limit reached!
% 7.38/2.96 % (1593460)------------------------------
% 7.38/2.96 % (1593460)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593460)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593460)Termination reason: Instruction limit
% 7.38/2.96 % (1593460)Termination phase: Property scanning
% 7.38/2.96 % (1593460)Time elapsed: 0.069 s
% 7.38/2.96 % (1593460)Peak memory usage: 112 MB
% 7.38/2.96 % (1593460)Instructions burned: 159 (million)
% 7.38/2.96 % (1593462)Instruction limit reached!
% 7.38/2.96 % (1593462)------------------------------
% 7.38/2.96 % (1593462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593462)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593462)Termination reason: Instruction limit
% 7.38/2.96 % (1593462)Termination phase: Property scanning
% 7.38/2.96 % (1593462)Time elapsed: 0.105 s
% 7.38/2.96 % (1593462)Peak memory usage: 112 MB
% 7.38/2.96 % (1593462)Instructions burned: 249 (million)
% 7.38/2.96 % (1593461)First to succeed.
% 7.38/2.96 % (1593461)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1593440"
% 7.38/2.96 % (1593459)Also succeeded, but the first one will report.
% 7.38/2.96 % (1593467)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1417170430:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2984 on theBenchmark for (2984ds/294Mi)
% 7.38/2.96 % (1593468)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3837225802:i=2350_2983 on theBenchmark for (2983ds/2350Mi)
% 7.38/2.96 % (1593467)Also succeeded, but the first one will report.
% 7.38/2.96 % (1593461)Refutation found. Thanks to Tanya!
% 7.38/2.96 % SZS status Theorem for theBenchmark
% 7.38/2.96 % SZS output start Proof for theBenchmark
% See solution above
% 7.38/2.96 % (1593461)------------------------------
% 7.38/2.96 % (1593461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.38/2.96 % (1593461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.38/2.96 % (1593461)CaDiCaL version: 2.1.3
% 7.38/2.96 % (1593461)Termination reason: Refutation
% 7.38/2.96 % (1593461)Time elapsed: 0.108 s
% 7.38/2.96 % (1593461)Peak memory usage: 118 MB
% 7.38/2.96 % (1593461)Instructions burned: 121 (million)
% 7.38/2.96 % (1593461)------------------------------
% 7.38/2.96 % (1593461)------------------------------
% 7.38/2.96 % (1593440)Success in time 1.896 s
% 7.38/2.96 % Vampire exiting
%------------------------------------------------------------------------------