%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:47:41 PM UTC 2026
% Result : Theorem 4.90s 6.67s
% Output : Refutation 4.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 72 ( 27 ~; 23 |; 14 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f112,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,X1)
& in(X0,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f113,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t116_relat_1) ).
fof(f114,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_rng_restriction(X0,X1)),X0) ),
inference(negated_conjecture,[status(cth)],[f113]) ).
fof(f194,plain,
? [X0,X1] :
( ~ subset(relation_rng(relation_rng_restriction(X0,X1)),X0)
& relation(X1) ),
inference(ennf_transformation,[],[f114]) ).
fof(f197,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f198,plain,
! [X0,X1,X2] :
( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,X1)
& in(X0,relation_rng(X2)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f112]) ).
fof(f205,plain,
( ~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),sK0)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f194]) ).
fof(f206,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f197]) ).
fof(f207,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f206]) ).
fof(f208,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f207]) ).
fof(f211,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(X2)) )
& ( ( in(X0,X1)
& in(X0,relation_rng(X2)) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f198]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ~ in(X0,X1)
| ~ in(X0,relation_rng(X2)) )
& ( ( in(X0,X1)
& in(X0,relation_rng(X2)) )
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f211]) ).
fof(f220,plain,
relation(sK1),
inference(cnf_transformation,[],[f205]) ).
fof(f221,plain,
~ subset(relation_rng(relation_rng_restriction(sK0,sK1)),sK0),
inference(cnf_transformation,[],[f205]) ).
fof(f225,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f226,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f208]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f212]) ).
fof(f257,plain,
in(sK2(relation_rng(relation_rng_restriction(sK0,sK1)),sK0),relation_rng(relation_rng_restriction(sK0,sK1))),
inference(unit_resulting_resolution,[],[f225,f221]) ).
fof(f259,plain,
~ in(sK2(relation_rng(relation_rng_restriction(sK0,sK1)),sK0),sK0),
inference(unit_resulting_resolution,[],[f226,f221]) ).
fof(f277,plain,
$false,
inference(unit_resulting_resolution,[],[f231,f220,f259,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU198+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 28 04:00:25 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/5.40 Running first-order theorem proving
% 0.14/5.40 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
% 4.90/6.67 % (420794)Detected formulas, will run a generic FOF schedule.
% 4.90/6.67 % (420801)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=1887177784:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.90/6.67 % (420799)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=3910868134:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.90/6.67 % (420803)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=595180066:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.90/6.67 % (420800)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=2557222876:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.90/6.67 % (420802)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1407825890:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.90/6.67 % (420804)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2903104022:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.90/6.67 % (420805)dis-21_1_sil=8000:lcm=predicate:random_seed=875688122:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.90/6.67 % (420802)Instruction limit reached!
% 4.90/6.67 % (420802)------------------------------
% 4.90/6.67 % (420802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420802)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420802)Termination reason: Instruction limit
% 4.90/6.67 % (420802)Termination phase: Saturation
% 4.90/6.67 % (420802)Time elapsed: 0.073 s
% 4.90/6.67 % (420802)Peak memory usage: 90 MB
% 4.90/6.67 % (420802)Instructions burned: 110 (million)
% 4.90/6.67 % (420803)Instruction limit reached!
% 4.90/6.67 % (420803)------------------------------
% 4.90/6.67 % (420803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420803)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420803)Termination reason: Instruction limit
% 4.90/6.67 % (420803)Termination phase: Saturation
% 4.90/6.67 % (420803)Time elapsed: 0.079 s
% 4.90/6.67 % (420803)Peak memory usage: 89 MB
% 4.90/6.67 % (420803)Instructions burned: 120 (million)
% 4.90/6.67 % (420805)Instruction limit reached!
% 4.90/6.67 % (420805)------------------------------
% 4.90/6.67 % (420805)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420805)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420805)Termination reason: Instruction limit
% 4.90/6.67 % (420805)Termination phase: Saturation
% 4.90/6.67 % (420805)Time elapsed: 0.076 s
% 4.90/6.67 % (420805)Peak memory usage: 90 MB
% 4.90/6.67 % (420805)Instructions burned: 130 (million)
% 4.90/6.67 % (420804)Instruction limit reached!
% 4.90/6.67 % (420804)------------------------------
% 4.90/6.67 % (420804)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420804)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420804)Termination reason: Instruction limit
% 4.90/6.67 % (420804)Termination phase: Saturation
% 4.90/6.67 % (420804)Time elapsed: 0.102 s
% 4.90/6.67 % (420804)Peak memory usage: 90 MB
% 4.90/6.67 % (420804)Instructions burned: 139 (million)
% 4.90/6.67 % (420814)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4219948888:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.90/6.67 % (420813)lrs+10_1_sil=8000:sp=occurrence:random_seed=461337672:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.90/6.67 % (420814)First to succeed.
% 4.90/6.67 % (420814)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-420794"
% 4.90/6.67 % (420815)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3467041132:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.90/6.67 % (420816)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=2461197825:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.90/6.67 % (420816)Also succeeded, but the first one will report.
% 4.90/6.67 % (420815)Also succeeded, but the first one will report.
% 4.90/6.67 % (420801)Also succeeded, but the first one will report.
% 4.90/6.67 % (420813)Instruction limit reached!
% 4.90/6.67 % (420813)------------------------------
% 4.90/6.67 % (420813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420813)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420813)Termination reason: Instruction limit
% 4.90/6.67 % (420813)Termination phase: Saturation
% 4.90/6.67 % (420813)Time elapsed: 0.185 s
% 4.90/6.67 % (420813)Peak memory usage: 92 MB
% 4.90/6.67 % (420813)Instructions burned: 286 (million)
% 4.90/6.67 % (420814)Refutation found. Thanks to Tanya!
% 4.90/6.67 % SZS status Theorem for theBenchmark
% 4.90/6.67 % SZS output start Proof for theBenchmark
% See solution above
% 4.90/6.67 % (420814)------------------------------
% 4.90/6.67 % (420814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.90/6.67 % (420814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.90/6.67 % (420814)CaDiCaL version: 2.1.3
% 4.90/6.67 % (420814)Termination reason: Refutation
% 4.90/6.67 % (420814)Time elapsed: 0.004 s
% 4.90/6.67 % (420814)Peak memory usage: 89 MB
% 4.90/6.67 % (420814)Instructions burned: 4 (million)
% 4.90/6.67 % (420814)------------------------------
% 4.90/6.67 % (420814)------------------------------
% 4.90/6.67 % (420794)Success in time 0.625 s
% 4.90/6.67 % Vampire exiting
%------------------------------------------------------------------------------