%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU188+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 : n026.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 02:55:48 PM UTC 2026
% Result : Theorem 3.08s 1.30s
% Output : CNFRefutation 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 14 unt; 2 def)
% Number of atoms : 126 ( 41 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 46 ~; 44 |; 11 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn 25 !; 2 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f20,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f21,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f31,conjecture,
! [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(f32,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f40,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(ennf_transformation,[],[f21]) ).
fof(f43,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(flattening,[],[f42]) ).
fof(f51,plain,
? [X0] :
( relation(X0)
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& empty_set != X0 ),
inference(ennf_transformation,[],[f32]) ).
fof(f52,plain,
? [X0] :
( relation(X0)
& ( relation_rng(X0) = empty_set
| relation_dom(X0) = empty_set )
& empty_set != X0 ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f33]) ).
fof(f55,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f68,plain,
( relation(sK13)
& ( empty_set = relation_rng(sK13)
| empty_set = relation_dom(sK13) )
& empty_set != sK13 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f52]) ).
fof(f87,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f88,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f89,plain,
! [X0] :
( ~ relation(X0)
| empty(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f103,plain,
relation(sK13),
inference(cnf_transformation,[],[f68]) ).
fof(f104,plain,
( empty_set = relation_rng(sK13)
| empty_set = relation_dom(sK13) ),
inference(cnf_transformation,[],[f68]) ).
fof(f105,plain,
empty_set != sK13,
inference(cnf_transformation,[],[f68]) ).
fof(f106,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f53]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_65,plain,
empty(empty_set),
inference(cnf_transformation,[],[f87]) ).
tcf(c_67,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_68,plain,
! [X0: $i] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_82,negated_conjecture,
empty_set != sK13,
inference(cnf_transformation,[],[f105]) ).
tcf(c_83,negated_conjecture,
( ( relation_rng(sK13) = empty_set )
| ( relation_dom(sK13) = empty_set ) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_84,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f103]) ).
tcf(c_85,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_2198,definition,
iPr_def_10 = relation_dom(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2199,definition,
iPr_def_11 = relation_rng(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2200,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_2201,negated_conjecture,
( ( iPr_def_11 = empty_set )
| ( iPr_def_10 = empty_set ) ),
inference(demodulation,[status(thm)],[c_83,c_2199,c_2198]) ).
tcf(c_2202,negated_conjecture,
empty_set != sK13,
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_2614,plain,
( empty(iPr_def_11)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2201,c_65]) ).
tcf(c_2801,plain,
( empty(sK13)
| ~ empty(iPr_def_10)
| ~ relation(sK13) ),
inference(superposition,[status(thm)],[c_2198,c_67]) ).
tcf(c_2805,plain,
( empty(sK13)
| ~ empty(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2801,c_2200]) ).
tcf(c_2815,plain,
( empty(sK13)
| ~ empty(iPr_def_11)
| ~ relation(sK13) ),
inference(superposition,[status(thm)],[c_2199,c_68]) ).
tcf(c_2818,plain,
( empty(sK13)
| ~ empty(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2815,c_2200]) ).
tcf(c_2859,plain,
( empty(sK13)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2614,c_2818]) ).
tcf(c_2869,plain,
( ( empty_set = iPr_def_10 )
| ( empty_set = sK13 ) ),
inference(superposition,[status(thm)],[c_2859,c_85]) ).
tcf(c_2879,plain,
empty_set = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_2869,c_2202]) ).
tcf(c_2888,plain,
empty(iPr_def_10),
inference(demodulation,[status(thm)],[c_65,c_2879]) ).
tcf(c_2891,plain,
empty(sK13),
inference(backward_subsumption_resolution,[status(thm)],[c_2805,c_2888]) ).
tcf(c_2905,plain,
! [X0: $i] :
( ( X0 = sK13 )
| ~ empty(X0) ),
inference(superposition,[status(thm)],[c_2891,c_87]) ).
tcf(c_2909,plain,
( ( empty_set = sK13 )
| ~ empty(empty_set) ),
inference(instantiation,[status(thm)],[c_2905]) ).
tcf(c_2910,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2909,c_82,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 13:09:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.08/1.30 % SZS status Started for theBenchmark.p
% 3.08/1.30 % SZS status Theorem for theBenchmark.p
% 3.08/1.30
% 3.08/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.08/1.30
% 3.08/1.30 % ------ iProver source info
% 3.08/1.30
% 3.08/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.08/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.08/1.30 % git: non_committed_changes: false
% 3.08/1.30
% 3.08/1.30 % ------ Parsing...
% 3.08/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.08/1.30
% 3.08/1.30 % ------ Preprocessing... sup_sim: 9 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.08/1.30
% 3.08/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.08/1.30
% 3.08/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.08/1.30 % ------ Proving...
% 3.08/1.30 % ------ Problem Properties
% 3.08/1.30
% 3.08/1.30 %
% 3.08/1.30 % clauses 37
% 3.08/1.30 % conjectures 3
% 3.08/1.30 % EPR 16
% 3.08/1.30 % Horn 32
% 3.08/1.30 % unary 15
% 3.08/1.30 % binary 10
% 3.08/1.30 % lits 75
% 3.08/1.30 % lits eq 13
% 3.08/1.30 % fd_pure 0
% 3.08/1.30 % fd_pseudo 0
% 3.08/1.30 % fd_cond 2
% 3.08/1.30 % fd_pseudo_cond 5
% 3.08/1.30 % AC symbols 0
% 3.08/1.30
% 3.08/1.30 % ------ Schedule dynamic 5 is on
% 3.08/1.30
% 3.08/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.08/1.30
% 3.08/1.30
% 3.08/1.30 % ------
% 3.08/1.30 % Current options:
% 3.08/1.30 % ------
% 3.08/1.30
% 3.08/1.30
% 3.08/1.30 %
% 3.08/1.30
% 3.08/1.30 % ------ Proving...
% 3.08/1.30 %
% 3.08/1.30
% 3.08/1.30 % SZS status Theorem for theBenchmark.p
% 3.08/1.30
% 3.08/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.08/1.30
% 3.08/1.30
%------------------------------------------------------------------------------