%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU422+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 : n018.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 6.76s 2.78s
% Output : Refutation 6.76s
% 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(f404,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(f425,axiom,
! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f677,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(f19085,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(f19086,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(f19087,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)],[f19086]) ).
fof(f19125,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,[],[f19087]) ).
fof(f19159,plain,
! [X0,X1] :
( r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f404]) ).
fof(f19160,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,[],[f19085]) ).
fof(f19383,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(ennf_transformation,[],[f70]) ).
fof(f19384,plain,
! [X0,X1,X2] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(flattening,[],[f19383]) ).
fof(f19522,plain,
( ~ m1_subset_1(a_2_0_relset_2(sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK2)))
& m1_subset_1(sK3,k1_zfmisc_1(sK2))
& ~ v1_xboole_0(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f19125]) ).
fof(f19542,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,[],[f677]) ).
fof(f19701,plain,
~ v1_xboole_0(sK2),
inference(cnf_transformation,[],[f19522]) ).
fof(f19702,plain,
m1_subset_1(sK3,k1_zfmisc_1(sK2)),
inference(cnf_transformation,[],[f19522]) ).
fof(f19703,plain,
~ m1_subset_1(a_2_0_relset_2(sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK2))),
inference(cnf_transformation,[],[f19522]) ).
fof(f19757,plain,
! [X0,X1] :
( ~ m1_subset_1(X0,k1_zfmisc_1(X1))
| r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f19542]) ).
fof(f19758,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f19542]) ).
fof(f19767,plain,
! [X0,X1] :
( r1_tarski(k1_zfmisc_1(X0),k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f19159]) ).
fof(f19772,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,[],[f19160]) ).
fof(f20116,plain,
! [X2,X0,X1] :
( r1_tarski(X0,X2)
| ~ r1_tarski(X0,X1)
| ~ r1_tarski(X1,X2) ),
inference(cnf_transformation,[],[f19384]) ).
fof(f20228,plain,
! [X0] : r1_tarski(X0,k1_zfmisc_1(k3_tarski(X0))),
inference(cnf_transformation,[],[f425]) ).
fof(f20649,plain,
r1_tarski(sK3,sK2),
inference(resolution,[],[f19702,f19757]) ).
fof(f20689,plain,
~ r1_tarski(a_2_0_relset_2(sK2,sK3),k1_zfmisc_1(sK2)),
inference(resolution,[],[f19703,f19758]) ).
fof(f20706,plain,
! [X0] :
( ~ r1_tarski(a_2_0_relset_2(sK2,sK3),X0)
| ~ r1_tarski(X0,k1_zfmisc_1(sK2)) ),
inference(resolution,[],[f20689,f20116]) ).
fof(f20795,plain,
~ r1_tarski(k1_zfmisc_1(k3_tarski(a_2_0_relset_2(sK2,sK3))),k1_zfmisc_1(sK2)),
inference(resolution,[],[f20706,f20228]) ).
fof(f20943,plain,
( ~ r1_tarski(k1_zfmisc_1(sK3),k1_zfmisc_1(sK2))
| ~ m1_subset_1(sK3,k1_zfmisc_1(sK2))
| v1_xboole_0(sK2) ),
inference(superposition,[],[f20795,f19772]) ).
fof(f20947,plain,
( ~ r1_tarski(k1_zfmisc_1(sK3),k1_zfmisc_1(sK2))
| v1_xboole_0(sK2) ),
inference(forward_subsumption_resolution,[],[f20943,f19702]) ).
fof(f20957,plain,
~ r1_tarski(k1_zfmisc_1(sK3),k1_zfmisc_1(sK2)),
inference(forward_subsumption_resolution,[],[f20947,f19701]) ).
fof(f21008,plain,
~ r1_tarski(sK3,sK2),
inference(resolution,[],[f20957,f19767]) ).
fof(f21010,plain,
$false,
inference(forward_subsumption_resolution,[],[f21008,f20649]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU422+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:20:59 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 5.51/2.69 % (3025013)Detected formulas, will run a generic FOF schedule.
% 5.51/2.69 % (3025022)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2424039022:i=119:av=off:ss=axioms_2988 on theBenchmark for (2988ds/119Mi)
% 5.51/2.69 % (3025020)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=3912715434:i=141695:sd=1:nm=32:gsp=on:ss=included_2988 on theBenchmark for (2988ds/141695Mi)
% 5.51/2.69 % (3025019)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=807816913:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2988 on theBenchmark for (2988ds/134677Mi)
% 5.51/2.69 % (3025018)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=195449960:i=141193_2988 on theBenchmark for (2988ds/141193Mi)
% 5.51/2.69 % (3025021)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3626193644:i=109:sd=1:ins=1:gsp=on:ss=axioms_2988 on theBenchmark for (2988ds/109Mi)
% 5.51/2.69 % (3025023)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1186011485:s2a=on:i=139:gtg=position_2988 on theBenchmark for (2988ds/139Mi)
% 5.51/2.69 % (3025024)dis-21_1_sil=8000:lcm=predicate:random_seed=1012654764: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)
% 5.51/2.69 % (3025022)Instruction limit reached!
% 5.51/2.69 % (3025022)------------------------------
% 5.51/2.69 % (3025022)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.51/2.69 % (3025022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/2.69 % (3025022)CaDiCaL version: 2.1.3
% 5.51/2.69 % (3025022)Termination reason: Instruction limit
% 5.51/2.69 % (3025022)Termination phase: Naming
% 5.51/2.69 % (3025022)Time elapsed: 0.063 s
% 5.51/2.69 % (3025022)Peak memory usage: 114 MB
% 5.51/2.69 % (3025022)Instructions burned: 121 (million)
% 5.51/2.69 % (3025023)Instruction limit reached!
% 5.51/2.69 % (3025023)------------------------------
% 5.51/2.69 % (3025023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.51/2.69 % (3025023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/2.69 % (3025023)CaDiCaL version: 2.1.3
% 5.51/2.69 % (3025023)Termination reason: Instruction limit
% 5.51/2.69 % (3025023)Termination phase: Property scanning
% 5.51/2.69 % (3025023)Time elapsed: 0.060 s
% 5.51/2.69 % (3025023)Peak memory usage: 112 MB
% 5.51/2.69 % (3025023)Instructions burned: 140 (million)
% 5.51/2.69 % (3025021)Instruction limit reached!
% 5.51/2.69 % (3025021)------------------------------
% 5.51/2.69 % (3025021)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.51/2.69 % (3025021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/2.69 % (3025021)CaDiCaL version: 2.1.3
% 5.51/2.69 % (3025021)Termination reason: Instruction limit
% 5.51/2.69 % (3025021)Termination phase: SInE selection
% 5.51/2.69 % (3025021)Time elapsed: 0.083 s
% 5.51/2.69 % (3025021)Peak memory usage: 112 MB
% 5.51/2.69 % (3025021)Instructions burned: 110 (million)
% 5.51/2.69 % (3025024)Instruction limit reached!
% 5.51/2.69 % (3025024)------------------------------
% 5.51/2.69 % (3025024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.51/2.69 % (3025024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.51/2.69 % (3025024)CaDiCaL version: 2.1.3
% 5.51/2.69 % (3025024)Termination reason: Instruction limit
% 5.51/2.69 % (3025024)Termination phase: SInE selection
% 5.51/2.69 % (3025024)Time elapsed: 0.088 s
% 5.51/2.69 % (3025024)Peak memory usage: 112 MB
% 5.51/2.69 % (3025024)Instructions burned: 130 (million)
% 5.51/2.69 % (3025032)lrs+10_1_sil=8000:sp=occurrence:random_seed=3516427716:i=285:sd=3:ss=axioms:sgt=8_2987 on theBenchmark for (2987ds/285Mi)
% 5.51/2.69 % (3025033)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3340652977:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2986 on theBenchmark for (2986ds/157Mi)
% 5.51/2.69 % (3025034)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1078869553:i=325:sd=1:ss=axioms:sgt=32_2986 on theBenchmark for (2986ds/325Mi)
% 5.51/2.69 % (3025032)Instruction limit reached!
% 5.51/2.69 % (3025032)------------------------------
% 5.51/2.69 % (3025032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.51/2.69 % (3025032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.78 % (3025032)CaDiCaL version: 2.1.3
% 6.76/2.78 % (3025032)Termination reason: Instruction limit
% 6.76/2.78 % (3025032)Termination phase: Saturation
% 6.76/2.78 % (3025032)Time elapsed: 0.127 s
% 6.76/2.78 % (3025032)Peak memory usage: 119 MB
% 6.76/2.78 % (3025032)Instructions burned: 288 (million)
% 6.76/2.78 % (3025035)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=2864713813:s2a=on:i=248:s2at=1.23:gtg=position_2986 on theBenchmark for (2986ds/248Mi)
% 6.76/2.78 % (3025033)Instruction limit reached!
% 6.76/2.78 % (3025033)------------------------------
% 6.76/2.78 % (3025033)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.78 % (3025033)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.78 % (3025033)CaDiCaL version: 2.1.3
% 6.76/2.78 % (3025033)Termination reason: Instruction limit
% 6.76/2.78 % (3025033)Termination phase: Property scanning
% 6.76/2.78 % (3025033)Time elapsed: 0.070 s
% 6.76/2.78 % (3025033)Peak memory usage: 112 MB
% 6.76/2.78 % (3025033)Instructions burned: 158 (million)
% 6.76/2.78 % (3025040)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2145783384:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2985 on theBenchmark for (2985ds/294Mi)
% 6.76/2.78 % (3025035)Instruction limit reached!
% 6.76/2.78 % (3025035)------------------------------
% 6.76/2.78 % (3025035)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.78 % (3025035)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.78 % (3025035)CaDiCaL version: 2.1.3
% 6.76/2.78 % (3025035)Termination reason: Instruction limit
% 6.76/2.78 % (3025035)Termination phase: Property scanning
% 6.76/2.78 % (3025035)Time elapsed: 0.108 s
% 6.76/2.78 % (3025035)Peak memory usage: 112 MB
% 6.76/2.78 % (3025035)Instructions burned: 248 (million)
% 6.76/2.78 % (3025041)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2667333668:i=2350_2984 on theBenchmark for (2984ds/2350Mi)
% 6.76/2.78 % (3025040)First to succeed.
% 6.76/2.78 % (3025040)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3025013"
% 6.76/2.78 % (3025034)Instruction limit reached!
% 6.76/2.78 % (3025034)------------------------------
% 6.76/2.78 % (3025034)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.78 % (3025034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.78 % (3025034)CaDiCaL version: 2.1.3
% 6.76/2.78 % (3025034)Termination reason: Instruction limit
% 6.76/2.78 % (3025034)Termination phase: Saturation
% 6.76/2.78 % (3025034)Time elapsed: 0.252 s
% 6.76/2.78 % (3025034)Peak memory usage: 118 MB
% 6.76/2.78 % (3025034)Instructions burned: 325 (million)
% 6.76/2.78 % (3025043)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=523961206:cts=off:i=113:fsr=off:ss=included:sgt=4_2984 on theBenchmark for (2984ds/113Mi)
% 6.76/2.78 % (3025040)Refutation found. Thanks to Tanya!
% 6.76/2.78 % SZS status Theorem for theBenchmark
% 6.76/2.78 % SZS output start Proof for theBenchmark
% See solution above
% 6.76/2.78 % (3025040)------------------------------
% 6.76/2.78 % (3025040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.78 % (3025040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.78 % (3025040)CaDiCaL version: 2.1.3
% 6.76/2.78 % (3025040)Termination reason: Refutation
% 6.76/2.78 % (3025040)Time elapsed: 0.098 s
% 6.76/2.78 % (3025040)Peak memory usage: 118 MB
% 6.76/2.78 % (3025040)Instructions burned: 241 (million)
% 6.76/2.78 % (3025040)------------------------------
% 6.76/2.78 % (3025040)------------------------------
% 6.76/2.78 % (3025013)Success in time 1.836 s
% 6.76/2.78 % Vampire exiting
%------------------------------------------------------------------------------