%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU188+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 : n012.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 12:47:38 PM UTC 2026
% Result : Theorem 2.35s 0.93s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 7 unt; 0 def)
% Number of atoms : 77 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 80 ( 34 ~; 30 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 16 ( 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f64,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f66,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f67,axiom,
! [X0] :
( ( ~ empty(X0)
& relation(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f156,conjecture,
! [X0] :
( relation(X0)
=> ( ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f157,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f156]) ).
fof(f160,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f241,plain,
? [X0] :
( empty_set != X0
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& relation(X0) ),
inference(ennf_transformation,[],[f157]) ).
fof(f242,plain,
? [X0] :
( empty_set != X0
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& relation(X0) ),
inference(flattening,[],[f241]) ).
fof(f249,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f160]) ).
fof(f267,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f268,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f267]) ).
fof(f271,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f272,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(flattening,[],[f271]) ).
fof(f325,plain,
( empty_set != sK6
& ( empty_set = relation_dom(sK6)
| empty_set = relation_rng(sK6) )
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f242]) ).
fof(f483,plain,
relation(sK6),
inference(cnf_transformation,[],[f325]) ).
fof(f484,plain,
( empty_set = relation_rng(sK6)
| empty_set = relation_dom(sK6) ),
inference(cnf_transformation,[],[f325]) ).
fof(f485,plain,
empty_set != sK6,
inference(cnf_transformation,[],[f325]) ).
fof(f498,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f500,plain,
empty(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f594,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f601,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f792,plain,
! [X0] :
( sK6 != X0
| ~ empty(X0) ),
inference(superposition,[],[f485,f498]) ).
fof(f796,plain,
~ empty(sK6),
inference(equality_resolution,[],[f792]) ).
fof(f934,plain,
( ~ empty(empty_set)
| empty(sK6)
| ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(superposition,[],[f601,f484]) ).
fof(f938,plain,
( empty(sK6)
| ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(forward_subsumption_resolution,[],[f934,f500]) ).
fof(f939,plain,
( ~ relation(sK6)
| empty_set = relation_dom(sK6) ),
inference(forward_subsumption_resolution,[],[f938,f796]) ).
fof(f940,plain,
empty_set = relation_dom(sK6),
inference(forward_subsumption_resolution,[],[f939,f483]) ).
fof(f942,plain,
( ~ empty(empty_set)
| empty(sK6)
| ~ relation(sK6) ),
inference(superposition,[],[f594,f940]) ).
fof(f946,plain,
( empty(sK6)
| ~ relation(sK6) ),
inference(forward_subsumption_resolution,[],[f942,f500]) ).
fof(f947,plain,
~ relation(sK6),
inference(forward_subsumption_resolution,[],[f946,f796]) ).
fof(f948,plain,
$false,
inference(forward_subsumption_resolution,[],[f947,f483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU188+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 28 03:57:34 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 2.35/0.93 % (3002318)Detected formulas, will run a generic FOF schedule.
% 2.35/0.93 % (3002327)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3218864775:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.35/0.93 % (3002326)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3985078082:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.35/0.93 % (3002324)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=2727668030:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.35/0.93 % (3002323)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=1650493806:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.35/0.93 % (3002329)dis-21_1_sil=8000:lcm=predicate:random_seed=89072366: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)
% 2.35/0.93 % (3002325)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=2587024444:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.35/0.93 % (3002328)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1170028491:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.35/0.93 % (3002327)First to succeed.
% 2.35/0.93 % (3002327)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3002318"
% 2.35/0.93 % (3002326)Also succeeded, but the first one will report.
% 2.35/0.93 % (3002328)Also succeeded, but the first one will report.
% 2.35/0.93 % (3002329)Instruction limit reached!
% 2.35/0.93 % (3002329)------------------------------
% 2.35/0.93 % (3002329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.93 % (3002329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.93 % (3002329)CaDiCaL version: 2.1.3
% 2.35/0.93 % (3002329)Termination reason: Instruction limit
% 2.35/0.93 % (3002329)Termination phase: Saturation
% 2.35/0.93 % (3002329)Time elapsed: 0.041 s
% 2.35/0.93 % (3002329)Peak memory usage: 90 MB
% 2.35/0.93 % (3002329)Instructions burned: 130 (million)
% 2.35/0.93 % (3002327)Refutation found. Thanks to Tanya!
% 2.35/0.93 % SZS status Theorem for theBenchmark
% 2.35/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.35/0.94 % (3002327)------------------------------
% 2.35/0.94 % (3002327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.35/0.94 % (3002327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.35/0.94 % (3002327)CaDiCaL version: 2.1.3
% 2.35/0.94 % (3002327)Termination reason: Refutation
% 2.35/0.94 % (3002327)Time elapsed: 0.006 s
% 2.35/0.94 % (3002327)Peak memory usage: 88 MB
% 2.35/0.94 % (3002327)Instructions burned: 16 (million)
% 2.35/0.94 % (3002327)------------------------------
% 2.35/0.94 % (3002327)------------------------------
% 2.35/0.94 % (3002318)Success in time 0.303 s
% 2.35/0.94 % Vampire exiting
%------------------------------------------------------------------------------