%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU154+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:47:27 PM UTC 2026
% Result : Theorem 3.65s 1.53s
% Output : Refutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 81 ( 24 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 99 ( 41 ~; 29 |; 25 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 37 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f33,conjecture,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f60,axiom,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X2] :
( in(X2,X0)
& in(X2,X1) )
& disjoint(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f83,plain,
! [X0,X1] :
( ~ ( ~ disjoint(X0,X1)
& ! [X2] :
~ ( in(X2,X0)
& in(X2,X1) ) )
& ~ ( ? [X3] :
( in(X3,X0)
& in(X3,X1) )
& disjoint(X0,X1) ) ),
inference(rectify,[],[f60]) ).
fof(f95,plain,
? [X0,X1] :
( ~ disjoint(singleton(X0),X1)
& ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f109,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ? [X2] :
( in(X2,X0)
& in(X2,X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f126,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f127,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f127]) ).
fof(f155,plain,
( ~ disjoint(singleton(sK8),sK9)
& ~ in(sK8,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f95]) ).
fof(f165,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| ( in(sK13(X0,X1),X0)
& in(sK13(X0,X1),X1) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X3,X1) )
| ~ disjoint(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X2,sK13(X0,X1))],[f109]) ).
fof(f176,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f225,plain,
~ in(sK8,sK9),
inference(cnf_transformation,[],[f155]) ).
fof(f226,plain,
~ disjoint(singleton(sK8),sK9),
inference(cnf_transformation,[],[f155]) ).
fof(f259,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK13(X0,X1),X1) ),
inference(cnf_transformation,[],[f165]) ).
fof(f260,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sK13(X0,X1),X0) ),
inference(cnf_transformation,[],[f165]) ).
fof(f285,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f176]) ).
fof(f337,plain,
in(sK13(singleton(sK8),sK9),sK9),
inference(resolution,[],[f259,f226]) ).
fof(f342,plain,
in(sK13(singleton(sK8),sK9),singleton(sK8)),
inference(resolution,[],[f260,f226]) ).
fof(f349,plain,
sK8 = sK13(singleton(sK8),sK9),
inference(resolution,[],[f342,f285]) ).
fof(f355,plain,
in(sK8,sK9),
inference(superposition,[],[f337,f349]) ).
fof(f356,plain,
$false,
inference(forward_subsumption_resolution,[],[f355,f225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU154+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n006.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % 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 03:47:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/1.53 % (3559028)Detected formulas, will run a generic FOF schedule.
% 3.65/1.53 % (3559047)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=323918714:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.65/1.53 % (3559049)dis-21_1_sil=8000:lcm=predicate:random_seed=2102649880: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)
% 3.65/1.53 % (3559043)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=3828203573:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.65/1.53 % (3559044)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=966182572:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.65/1.53 % (3559045)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=698620493:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.65/1.53 % (3559048)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=595492705:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.65/1.53 % (3559046)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3011497517:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.65/1.53 % (3559048)First to succeed.
% 3.65/1.53 % (3559047)Instruction limit reached!
% 3.65/1.53 % (3559047)------------------------------
% 3.65/1.53 % (3559047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.53 % (3559047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.53 % (3559047)CaDiCaL version: 2.1.3
% 3.65/1.53 % (3559047)Termination reason: Instruction limit
% 3.65/1.53 % (3559047)Termination phase: Saturation
% 3.65/1.53 % (3559047)Time elapsed: 0.043 s
% 3.65/1.53 % (3559047)Peak memory usage: 89 MB
% 3.65/1.53 % (3559047)Instructions burned: 121 (million)
% 3.65/1.53 % (3559048)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3559028"
% 3.65/1.53 % (3559046)Instruction limit reached!
% 3.65/1.53 % (3559046)------------------------------
% 3.65/1.53 % (3559046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.53 % (3559046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.53 % (3559046)CaDiCaL version: 2.1.3
% 3.65/1.53 % (3559046)Termination reason: Instruction limit
% 3.65/1.53 % (3559046)Termination phase: Saturation
% 3.65/1.53 % (3559046)Time elapsed: 0.073 s
% 3.65/1.53 % (3559046)Peak memory usage: 89 MB
% 3.65/1.53 % (3559046)Instructions burned: 109 (million)
% 3.65/1.53 % (3559049)Instruction limit reached!
% 3.65/1.53 % (3559049)------------------------------
% 3.65/1.53 % (3559049)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.53 % (3559049)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.53 % (3559049)CaDiCaL version: 2.1.3
% 3.65/1.53 % (3559049)Termination reason: Instruction limit
% 3.65/1.53 % (3559049)Termination phase: Saturation
% 3.65/1.53 % (3559049)Time elapsed: 0.086 s
% 3.65/1.53 % (3559049)Peak memory usage: 90 MB
% 3.65/1.53 % (3559049)Instructions burned: 129 (million)
% 3.65/1.53 % (3559101)lrs+10_1_sil=8000:sp=occurrence:random_seed=399827519:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.65/1.53 % (3559101)Also succeeded, but the first one will report.
% 3.65/1.53 % (3559132)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1081741362:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.65/1.53 % (3559131)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2169992976:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.65/1.53 % (3559131)Also succeeded, but the first one will report.
% 3.65/1.53 % (3559132)Also succeeded, but the first one will report.
% 3.65/1.53 % (3559048)Refutation found. Thanks to Tanya!
% 3.65/1.53 % SZS status Theorem for theBenchmark
% 3.65/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 3.65/1.53 % (3559048)------------------------------
% 3.65/1.53 % (3559048)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.65/1.53 % (3559048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.65/1.53 % (3559048)CaDiCaL version: 2.1.3
% 3.65/1.53 % (3559048)Termination reason: Refutation
% 3.65/1.53 % (3559048)Time elapsed: 0.006 s
% 3.65/1.53 % (3559048)Peak memory usage: 89 MB
% 3.65/1.53 % (3559048)Instructions burned: 7 (million)
% 3.65/1.53 % (3559048)------------------------------
% 3.65/1.53 % (3559048)------------------------------
% 3.65/1.53 % (3559028)Success in time 0.411 s
% 3.65/1.53 % Vampire exiting
%------------------------------------------------------------------------------