%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU162+1 : 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 : n004.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 12:47:30 PM UTC 2026
% Result : Theorem 3.64s 1.48s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 5 unt; 0 def)
% Number of atoms : 63 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 66 ( 33 ~; 23 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
~ ( disjoint(singleton(X0),X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f5,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f7,conjecture,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f10,plain,
? [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<~> ~ in(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f15,plain,
? [X0,X1] :
( ( in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f16,plain,
( ( in(sK1,sK0)
| sK0 != set_difference(sK0,singleton(sK1)) )
& ( ~ in(sK1,sK0)
| sK0 = set_difference(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f18,plain,
( sK0 = set_difference(sK0,singleton(sK1))
| ~ in(sK1,sK0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f19,plain,
( sK0 != set_difference(sK0,singleton(sK1))
| in(sK1,sK0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f22,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f25,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X1] :
( ~ disjoint(X1,singleton(X0))
| ~ in(X0,X1) ),
inference(resolution,[],[f23,f25]) ).
fof(f32,plain,
( sK0 != sK0
| in(sK1,sK0)
| ~ disjoint(sK0,singleton(sK1)) ),
inference(superposition,[],[f19,f20]) ).
fof(f33,plain,
( in(sK1,sK0)
| ~ disjoint(sK0,singleton(sK1)) ),
inference(trivial_inequality_removal,[],[f32]) ).
fof(f34,plain,
~ disjoint(sK0,singleton(sK1)),
inference(forward_subsumption_resolution,[],[f33,f29]) ).
fof(f35,plain,
~ disjoint(singleton(sK1),sK0),
inference(resolution,[],[f34,f25]) ).
fof(f36,plain,
in(sK1,sK0),
inference(resolution,[],[f35,f22]) ).
fof(f38,plain,
( sK0 != sK0
| disjoint(sK0,singleton(sK1))
| ~ in(sK1,sK0) ),
inference(superposition,[],[f21,f18]) ).
fof(f40,plain,
( disjoint(sK0,singleton(sK1))
| ~ in(sK1,sK0) ),
inference(trivial_inequality_removal,[],[f38]) ).
fof(f41,plain,
~ in(sK1,sK0),
inference(forward_subsumption_resolution,[],[f40,f29]) ).
fof(f44,plain,
$false,
inference(forward_subsumption_resolution,[],[f36,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n004.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 03:49:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.64/1.48 % (4132455)Detected formulas, will run a generic FOF schedule.
% 3.64/1.48 % (4132463)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3444695391:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.64/1.48 % (4132463)Refutation not found, incomplete strategy
% 3.64/1.48 % (4132463)------------------------------
% 3.64/1.48 % (4132463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.48 % (4132463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.48 % (4132463)CaDiCaL version: 2.1.3
% 3.64/1.48 % (4132463)Termination reason: Refutation not found, incomplete strategy
% 3.64/1.48 % (4132463)Time elapsed: 0.001 s
% 3.64/1.48 % (4132463)Peak memory usage: 88 MB
% 3.64/1.48 % (4132466)dis-21_1_sil=8000:lcm=predicate:random_seed=3175283163: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)
% 3.64/1.48 % (4132464)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2901689673:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.64/1.48 % (4132462)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=1772133903:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.64/1.48 % (4132460)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=2897798112:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.64/1.48 % (4132461)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=3953563726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.64/1.48 % (4132465)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2325371208:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.64/1.48 % (4132464)First to succeed.
% 3.64/1.48 % (4132466)Also succeeded, but the first one will report.
% 3.64/1.48 % (4132465)Also succeeded, but the first one will report.
% 3.64/1.48 % (4132464)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4132455"
% 3.64/1.48 % (4132463)------------------------------
% 3.64/1.48 % (4132463)------------------------------
% 3.64/1.48 % (4132474)lrs+10_1_sil=8000:sp=occurrence:random_seed=3122061873:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.64/1.48 % (4132464)Refutation found. Thanks to Tanya!
% 3.64/1.48 % SZS status Theorem for theBenchmark
% 3.64/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.48 % (4132464)------------------------------
% 3.64/1.48 % (4132464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.48 % (4132464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.48 % (4132464)CaDiCaL version: 2.1.3
% 3.64/1.48 % (4132464)Termination reason: Refutation
% 3.64/1.48 % (4132464)Time elapsed: 0.002 s
% 3.64/1.48 % (4132464)Peak memory usage: 88 MB
% 3.64/1.48 % (4132464)Instructions burned: 1 (million)
% 3.64/1.48 % (4132464)------------------------------
% 3.64/1.48 % (4132464)------------------------------
% 3.64/1.48 % (4132455)Success in time 0.439 s
% 3.64/1.48 % Vampire exiting
%------------------------------------------------------------------------------