%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 02:55:49 PM UTC 2026
% Result : Theorem 1.34s 1.27s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 81 ( 65 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 31 |; 10 &)
% ( 2 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 14 ( 0 sgn 11 !; 3 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f23,conjecture,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( relation_dom(X0) = empty_set
<=> relation_rng(X0) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f26,axiom,
! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f41,plain,
? [X0] :
( relation(X0)
& ( relation_dom(X0) = empty_set
<~> relation_rng(X0) = empty_set ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| ( relation_rng(X0) != empty_set
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(ennf_transformation,[],[f26]) ).
fof(f43,plain,
! [X0] :
( ~ relation(X0)
| ( relation_rng(X0) != empty_set
& relation_dom(X0) != empty_set )
| X0 = empty_set ),
inference(flattening,[],[f42]) ).
fof(f49,plain,
? [X0] :
( relation(X0)
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& ( relation_dom(X0) != empty_set
| relation_rng(X0) != empty_set ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f50,plain,
? [X0] :
( relation(X0)
& ( relation_dom(X0) = empty_set
| relation_rng(X0) = empty_set )
& ( relation_dom(X0) != empty_set
| relation_rng(X0) != empty_set ) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
( relation(sK5)
& ( empty_set = relation_dom(sK5)
| empty_set = relation_rng(sK5) )
& ( empty_set != relation_dom(sK5)
| empty_set != relation_rng(sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f50]) ).
fof(f75,plain,
relation(sK5),
inference(cnf_transformation,[],[f51]) ).
fof(f76,plain,
( empty_set = relation_dom(sK5)
| empty_set = relation_rng(sK5) ),
inference(cnf_transformation,[],[f51]) ).
fof(f77,plain,
( empty_set != relation_dom(sK5)
| empty_set != relation_rng(sK5) ),
inference(cnf_transformation,[],[f51]) ).
fof(f78,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f79,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f25]) ).
fof(f80,plain,
! [X0] :
( ~ relation(X0)
| relation_rng(X0) != empty_set
| empty_set = X0 ),
inference(cnf_transformation,[],[f43]) ).
fof(f81,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| empty_set = X0 ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_72,negated_conjecture,
( ( relation_rng(sK5) != empty_set )
| ( relation_dom(sK5) != empty_set ) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_73,negated_conjecture,
( ( relation_rng(sK5) = empty_set )
| ( relation_dom(sK5) = empty_set ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_74,negated_conjecture,
relation(sK5),
inference(cnf_transformation,[],[f75]) ).
tcf(c_75,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[],[f79]) ).
tcf(c_76,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[],[f78]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_dom(X0) != empty_set ) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_78,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ relation(X0)
| ( relation_rng(X0) != empty_set ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_489,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( X0 != sK5 )
| ( relation_rng(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_74]) ).
tcf(c_490,plain,
( ( sK5 = empty_set )
| ( relation_rng(sK5) != empty_set ) ),
inference(unflattening,[status(thm)],[c_489]) ).
tcf(c_497,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ( X0 != sK5 )
| ( relation_dom(X0) != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_74]) ).
tcf(c_498,plain,
( ( sK5 = empty_set )
| ( relation_dom(sK5) != empty_set ) ),
inference(unflattening,[status(thm)],[c_497]) ).
tcf(c_499,plain,
sK5 = empty_set,
inference(global_subsumption_just,[status(thm)],[c_498,c_73,c_490,c_498]) ).
tcf(c_547,plain,
( ( relation_dom(sK5) != empty_set )
| ( relation_rng(sK5) != empty_set ) ),
inference(prop_impl_just,[status(thm)],[c_72]) ).
tcf(c_548,plain,
( ( relation_rng(sK5) != empty_set )
| ( relation_dom(sK5) != empty_set ) ),
inference(renaming,[status(thm)],[c_547]) ).
tcf(c_793,plain,
empty_set != empty_set,
inference(light_normalisation,[status(thm)],[c_548,c_75,c_76,c_499]) ).
tcf(c_794,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:06:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.34/1.27 % SZS status Started for theBenchmark.p
% 1.34/1.27 % SZS status Theorem for theBenchmark.p
% 1.34/1.27
% 1.34/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.34/1.27
% 1.34/1.27 % ------ iProver source info
% 1.34/1.27
% 1.34/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.34/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.34/1.27 % git: non_committed_changes: false
% 1.34/1.27
% 1.34/1.27 % ------ Parsing...
% 1.34/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.34/1.27
% 1.34/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 1.34/1.27
% 1.34/1.27 % SZS status Theorem for theBenchmark.p
% 1.34/1.27
% 1.34/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.34/1.27
% 1.34/1.27
%------------------------------------------------------------------------------