%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU422+2 : 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 : n013.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 12:48:54 PM UTC 2026
% Result : Theorem 11.45s 3.10s
% Output : Refutation 11.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 67 ( 3 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 68 ( 33 ~; 20 |; 6 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f70,axiom,
! [X0,X1,X2] :
( ( r1_tarski(X0,X1)
& r1_tarski(X1,X2) )
=> r1_tarski(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f267,axiom,
! [X0,X1] :
( r1_tarski(X0,X1)
=> r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t79_zfmisc_1) ).
fof(f288,axiom,
! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f540,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f4486,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> X1 = k3_tarski(a_2_0_relset_2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_relset_2) ).
fof(f4487,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_2) ).
fof(f4488,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(X0))
=> m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0))) ) ),
inference(negated_conjecture,[status(cth)],[f4487]) ).
fof(f4531,plain,
? [X0] :
( ? [X1] :
( ~ m1_subset_1(a_2_0_relset_2(X0,X1),k1_zfmisc_1(k1_zfmisc_1(X0)))
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4488]) ).
fof(f4607,plain,
! [X0,X1] :
( r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f267]) ).
fof(f4608,plain,
! [X0] :
( ! [X1] :
( X1 = k3_tarski(a_2_0_relset_2(X0,X1))
| ~ m1_subset_1(X1,k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4486]) ).
fof(f5236,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(ennf_transformation,[],[f70]) ).
fof(f5237,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(flattening,[],[f5236]) ).
fof(f5495,plain,
( ~ m1_subset_1(a_2_0_relset_2(sK6,sK7),k1_zfmisc_1(k1_zfmisc_1(sK6)))
& m1_subset_1(sK7,k1_zfmisc_1(sK6))
& ~ v1_xboole_0(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f4531]) ).
fof(f5514,plain,
! [X0,X1] :
( ( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
& ( r1_tarski(X0,X1)
| ~ m1_subset_1(X0,k1_zfmisc_1(X1)) ) ),
inference(nnf_transformation,[],[f540]) ).
fof(f5839,plain,
~ v1_xboole_0(sK6),
inference(cnf_transformation,[],[f5495]) ).
fof(f5840,plain,
m1_subset_1(sK7,k1_zfmisc_1(sK6)),
inference(cnf_transformation,[],[f5495]) ).
fof(f5841,plain,
~ m1_subset_1(a_2_0_relset_2(sK6,sK7),k1_zfmisc_1(k1_zfmisc_1(sK6))),
inference(cnf_transformation,[],[f5495]) ).
fof(f5918,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f5514]) ).
fof(f5919,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f5514]) ).
fof(f5960,plain,
! [X0,X1] :
( r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f4607]) ).
fof(f5967,plain,
! [X0,X1] :
( k3_tarski(a_2_0_relset_2(X0,X1)) = X1
| ~ m1_subset_1(X1,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f4608]) ).
fof(f6913,plain,
! [X2,X0,X1] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(cnf_transformation,[],[f5237]) ).
fof(f7275,plain,
! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
inference(cnf_transformation,[],[f288]) ).
fof(f8019,plain,
r1_tarski(sK7,sK6),
inference(resolution,[],[f5840,f5918]) ).
fof(f8046,plain,
~ r1_tarski(a_2_0_relset_2(sK6,sK7),k1_zfmisc_1(sK6)),
inference(resolution,[],[f5841,f5919]) ).
fof(f8095,plain,
! [X0] :
( ~ r1_tarski(a_2_0_relset_2(sK6,sK7),X0)
| ~ r1_tarski(X0,k1_zfmisc_1(sK6)) ),
inference(resolution,[],[f8046,f6913]) ).
fof(f8267,plain,
~ r1_tarski(k1_zfmisc_1(k3_tarski(a_2_0_relset_2(sK6,sK7))),k1_zfmisc_1(sK6)),
inference(resolution,[],[f8095,f7275]) ).
fof(f8594,plain,
( ~ r1_tarski(k1_zfmisc_1(sK7),k1_zfmisc_1(sK6))
| ~ m1_subset_1(sK7,k1_zfmisc_1(sK6))
| v1_xboole_0(sK6) ),
inference(superposition,[],[f8267,f5967]) ).
fof(f8597,plain,
( ~ r1_tarski(k1_zfmisc_1(sK7),k1_zfmisc_1(sK6))
| v1_xboole_0(sK6) ),
inference(forward_subsumption_resolution,[],[f8594,f5840]) ).
fof(f8607,plain,
~ r1_tarski(k1_zfmisc_1(sK7),k1_zfmisc_1(sK6)),
inference(forward_subsumption_resolution,[],[f8597,f5839]) ).
fof(f9329,plain,
~ r1_tarski(sK7,sK6),
inference(resolution,[],[f8607,f5960]) ).
fof(f9331,plain,
$false,
inference(forward_subsumption_resolution,[],[f9329,f8019]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU422+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n013.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 28 05:18:07 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 9.55/2.80 % (840330)Detected formulas, will run a generic FOF schedule.
% 9.55/2.80 % (840337)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=769660189:i=141193_2997 on theBenchmark for (2997ds/141193Mi)
% 9.55/2.80 % (840339)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=530517061:i=141695:sd=1:nm=32:gsp=on:ss=included_2997 on theBenchmark for (2997ds/141695Mi)
% 9.55/2.80 % (840338)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=3735333090:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2997 on theBenchmark for (2997ds/134677Mi)
% 9.55/2.80 % (840342)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1857741332:s2a=on:i=139:gtg=position_2997 on theBenchmark for (2997ds/139Mi)
% 9.55/2.80 % (840340)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=370379373:i=109:sd=1:ins=1:gsp=on:ss=axioms_2997 on theBenchmark for (2997ds/109Mi)
% 9.55/2.80 % (840343)dis-21_1_sil=8000:lcm=predicate:random_seed=3102961211:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2997 on theBenchmark for (2997ds/129Mi)
% 9.55/2.80 % (840341)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3311406635:i=119:av=off:ss=axioms_2997 on theBenchmark for (2997ds/119Mi)
% 9.55/2.80 % (840340)Refutation not found, incomplete strategy
% 9.55/2.80 % (840340)------------------------------
% 9.55/2.80 % (840340)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.80 % (840340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.55/2.80 % (840340)CaDiCaL version: 2.1.3
% 9.55/2.80 % (840340)Termination reason: Refutation not found, incomplete strategy
% 9.55/2.80 % (840340)Time elapsed: 0.035 s
% 9.55/2.80 % (840340)Peak memory usage: 93 MB
% 9.55/2.80 % (840340)Instructions burned: 29 (million)
% 9.55/2.80 % (840341)Instruction limit reached!
% 9.55/2.80 % (840341)------------------------------
% 9.55/2.80 % (840341)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.80 % (840341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.55/2.80 % (840341)CaDiCaL version: 2.1.3
% 9.55/2.80 % (840341)Termination reason: Instruction limit
% 9.55/2.80 % (840341)Termination phase: Saturation
% 9.55/2.80 % (840341)Time elapsed: 0.132 s
% 9.55/2.80 % (840341)Peak memory usage: 94 MB
% 9.55/2.80 % (840341)Instructions burned: 119 (million)
% 9.55/2.80 % (840343)Instruction limit reached!
% 9.55/2.80 % (840343)------------------------------
% 9.55/2.80 % (840343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.80 % (840343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.55/2.80 % (840343)CaDiCaL version: 2.1.3
% 9.55/2.80 % (840343)Termination reason: Instruction limit
% 9.55/2.80 % (840343)Termination phase: Clausification
% 9.55/2.80 % (840343)Time elapsed: 0.138 s
% 9.55/2.80 % (840343)Peak memory usage: 95 MB
% 9.55/2.80 % (840343)Instructions burned: 129 (million)
% 9.55/2.80 % (840342)Instruction limit reached!
% 9.55/2.80 % (840342)------------------------------
% 9.55/2.80 % (840342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.80 % (840342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.55/2.80 % (840342)CaDiCaL version: 2.1.3
% 9.55/2.80 % (840342)Termination reason: Instruction limit
% 9.55/2.80 % (840342)Termination phase: Preprocessing 3
% 9.55/2.80 % (840342)Time elapsed: 0.142 s
% 9.55/2.80 % (840342)Peak memory usage: 94 MB
% 9.55/2.80 % (840342)Instructions burned: 139 (million)
% 9.55/2.80 % (840353)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2078102837:i=325:sd=1:ss=axioms:sgt=32_2993 on theBenchmark for (2993ds/325Mi)
% 9.55/2.80 % (840351)lrs+10_1_sil=8000:sp=occurrence:random_seed=2858736954:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 9.55/2.80 % (840352)lrs+10_1_sil=32000:urr=on:br=off:random_seed=869095020:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/157Mi)
% 9.55/2.80 % (840340)------------------------------
% 9.55/2.80 % (840340)------------------------------
% 9.55/2.80 % (840352)Instruction limit reached!
% 9.55/2.80 % (840352)------------------------------
% 9.55/2.80 % (840352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.55/2.80 % (840352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840352)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840352)Termination reason: Instruction limit
% 11.45/3.10 % (840352)Termination phase: Saturation
% 11.45/3.10 % (840352)Time elapsed: 0.155 s
% 11.45/3.10 % (840352)Peak memory usage: 93 MB
% 11.45/3.10 % (840352)Instructions burned: 158 (million)
% 11.45/3.10 % (840353)Instruction limit reached!
% 11.45/3.10 % (840353)------------------------------
% 11.45/3.10 % (840353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.45/3.10 % (840353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840353)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840353)Termination reason: Instruction limit
% 11.45/3.10 % (840353)Termination phase: Saturation
% 11.45/3.10 % (840353)Time elapsed: 0.304 s
% 11.45/3.10 % (840353)Peak memory usage: 95 MB
% 11.45/3.10 % (840353)Instructions burned: 325 (million)
% 11.45/3.10 % (840351)Instruction limit reached!
% 11.45/3.10 % (840351)------------------------------
% 11.45/3.10 % (840351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.45/3.10 % (840351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840351)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840351)Termination reason: Instruction limit
% 11.45/3.10 % (840351)Termination phase: Saturation
% 11.45/3.10 % (840351)Time elapsed: 0.307 s
% 11.45/3.10 % (840351)Peak memory usage: 96 MB
% 11.45/3.10 % (840351)Instructions burned: 285 (million)
% 11.45/3.10 % (840357)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=4230603910:s2a=on:i=248:s2at=1.23:gtg=position_2990 on theBenchmark for (2990ds/248Mi)
% 11.45/3.10 % (840358)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3849096627:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2988 on theBenchmark for (2988ds/294Mi)
% 11.45/3.10 % (840359)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3235950799:i=2350_2988 on theBenchmark for (2988ds/2350Mi)
% 11.45/3.10 % (840358)First to succeed.
% 11.45/3.10 % (840358)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-840330"
% 11.45/3.10 % (840357)Instruction limit reached!
% 11.45/3.10 % (840357)------------------------------
% 11.45/3.10 % (840357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.45/3.10 % (840357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840357)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840357)Termination reason: Instruction limit
% 11.45/3.10 % (840357)Termination phase: Property scanning
% 11.45/3.10 % (840357)Time elapsed: 0.254 s
% 11.45/3.10 % (840357)Peak memory usage: 98 MB
% 11.45/3.10 % (840357)Instructions burned: 248 (million)
% 11.45/3.10 % (840360)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2644605610:cts=off:i=113:fsr=off:ss=included:sgt=4_2987 on theBenchmark for (2987ds/113Mi)
% 11.45/3.10 % (840360)Instruction limit reached!
% 11.45/3.10 % (840360)------------------------------
% 11.45/3.10 % (840360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.45/3.10 % (840360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840360)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840360)Termination reason: Instruction limit
% 11.45/3.10 % (840360)Termination phase: Saturation
% 11.45/3.10 % (840360)Time elapsed: 0.115 s
% 11.45/3.10 % (840360)Peak memory usage: 95 MB
% 11.45/3.10 % (840360)Instructions burned: 113 (million)
% 11.45/3.10 % (840358)Refutation found. Thanks to Tanya!
% 11.45/3.10 % SZS status Theorem for theBenchmark
% 11.45/3.10 % SZS output start Proof for theBenchmark
% See solution above
% 11.45/3.10 % (840358)------------------------------
% 11.45/3.10 % (840358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.45/3.10 % (840358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.45/3.10 % (840358)CaDiCaL version: 2.1.3
% 11.45/3.10 % (840358)Termination reason: Refutation
% 11.45/3.10 % (840358)Time elapsed: 0.137 s
% 11.45/3.10 % (840358)Peak memory usage: 96 MB
% 11.45/3.10 % (840358)Instructions burned: 250 (million)
% 11.45/3.10 % (840358)------------------------------
% 11.45/3.10 % (840358)------------------------------
% 11.45/3.10 % (840330)Success in time 1.748 s
% 11.45/3.10 % Vampire exiting
%------------------------------------------------------------------------------