%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU355+1 : 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 : n008.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 12:48:30 PM UTC 2026
% Result : Theorem 3.53s 1.39s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 151 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 202 ( 84 ~; 75 |; 25 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 70 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).
fof(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f20,conjecture,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_set_smaller(X0,empty_set,X1)
& relstr_element_smaller(X0,empty_set,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f24,plain,
? [X0] :
( ? [X1] :
( ( ~ relstr_set_smaller(X0,empty_set,X1)
| ~ relstr_element_smaller(X0,empty_set,X1) )
& element(X1,the_carrier(X0)) )
& rel_str(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f28,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f29,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f31,plain,
! [X0] :
( ! [X1,X2] :
( ( relstr_set_smaller(X0,X1,X2)
<=> ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f34,plain,
( ( ~ relstr_set_smaller(sK0,empty_set,sK1)
| ~ relstr_element_smaller(sK0,empty_set,sK1) )
& element(sK1,the_carrier(sK0))
& rel_str(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f24]) ).
fof(f37,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f38,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X2,X3)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_element_smaller(X0,X1,X2)
| ( ~ related(X0,X2,sK4(X0,X1,X2))
& in(sK4(X0,X1,X2),X1)
& element(sK4(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X2,X4)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_element_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( related(X0,X3,X2)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(nnf_transformation,[],[f31]) ).
fof(f41,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ? [X3] :
( ~ related(X0,X3,X2)
& in(X3,X1)
& element(X3,the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X1,X2] :
( ( ( relstr_set_smaller(X0,X1,X2)
| ( ~ related(X0,sK5(X0,X1,X2),X2)
& in(sK5(X0,X1,X2),X1)
& element(sK5(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X4] :
( related(X0,X4,X2)
| ~ in(X4,X1)
| ~ element(X4,the_carrier(X0)) )
| ~ relstr_set_smaller(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ rel_str(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f41]) ).
fof(f45,plain,
rel_str(sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f46,plain,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f34]) ).
fof(f47,plain,
( ~ relstr_set_smaller(sK0,empty_set,sK1)
| ~ relstr_element_smaller(sK0,empty_set,sK1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f48,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(sK4(X0,X1,X2),X1)
| relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f59,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X1)
| relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f70,plain,
! [X2,X0,X1] :
( relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ empty(X1) ),
inference(resolution,[],[f55,f63]) ).
fof(f76,plain,
! [X2,X0,X1] :
( relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ rel_str(X0)
| ~ empty(X1) ),
inference(resolution,[],[f59,f63]) ).
fof(f83,plain,
( ~ element(sK1,the_carrier(sK0))
| ~ rel_str(sK0)
| ~ empty(empty_set)
| ~ relstr_element_smaller(sK0,empty_set,sK1) ),
inference(resolution,[],[f76,f47]) ).
fof(f84,plain,
( ~ element(sK1,the_carrier(sK0))
| ~ rel_str(sK0)
| ~ empty(empty_set) ),
inference(forward_subsumption_resolution,[],[f83,f70]) ).
fof(f85,plain,
( ~ rel_str(sK0)
| ~ empty(empty_set) ),
inference(forward_subsumption_resolution,[],[f84,f46]) ).
fof(f86,plain,
~ empty(empty_set),
inference(forward_subsumption_resolution,[],[f85,f45]) ).
fof(f87,plain,
$false,
inference(forward_subsumption_resolution,[],[f86,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU355+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n008.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 04:54:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.53/1.39 % (1885410)Detected formulas, will run a generic FOF schedule.
% 3.53/1.39 % (1885415)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=3642213461:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.39 % (1885420)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1647242381:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.39 % (1885417)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=2687703915:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.39 % (1885419)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3514481686:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.39 % (1885416)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=29995496:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.39 % (1885418)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3872055809:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.39 % (1885421)dis-21_1_sil=8000:lcm=predicate:random_seed=2216612364: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)
% 3.53/1.39 % (1885418)Refutation not found, incomplete strategy
% 3.53/1.39 % (1885418)------------------------------
% 3.53/1.39 % (1885418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.39 % (1885418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.39 % (1885418)CaDiCaL version: 2.1.3
% 3.53/1.39 % (1885418)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.39 % (1885418)Time elapsed: 0.002 s
% 3.53/1.39 % (1885419)First to succeed.
% 3.53/1.39 % (1885418)Peak memory usage: 88 MB
% 3.53/1.39 % (1885418)Instructions burned: 1 (million)
% 3.53/1.39 % (1885421)Also succeeded, but the first one will report.
% 3.53/1.39 % (1885419)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1885410"
% 3.53/1.39 % (1885420)Also succeeded, but the first one will report.
% 3.53/1.39 % (1885418)------------------------------
% 3.53/1.39 % (1885418)------------------------------
% 3.53/1.39 % (1885419)Refutation found. Thanks to Tanya!
% 3.53/1.39 % SZS status Theorem for theBenchmark
% 3.53/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.39 % (1885419)------------------------------
% 3.53/1.39 % (1885419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.39 % (1885419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.39 % (1885419)CaDiCaL version: 2.1.3
% 3.53/1.39 % (1885419)Termination reason: Refutation
% 3.53/1.39 % (1885419)Time elapsed: 0.003 s
% 3.53/1.39 % (1885419)Peak memory usage: 88 MB
% 3.53/1.39 % (1885419)Instructions burned: 2 (million)
% 3.53/1.39 % (1885419)------------------------------
% 3.53/1.39 % (1885419)------------------------------
% 3.53/1.39 % (1885410)Success in time 0.431 s
% 3.53/1.39 % Vampire exiting
%------------------------------------------------------------------------------