%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU321+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 : n007.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 02:56:51 PM UTC 2026
% Result : Theorem 1.96s 1.29s
% Output : CNFRefutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 21 unt; 2 def)
% Number of atoms : 202 ( 13 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 194 ( 81 ~; 65 |; 32 &)
% ( 2 <=>; 12 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f33,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f34,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_membered) ).
fof(f40,conjecture,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l40_tops_1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,subset_complement(the_carrier(X0),X1))
<=> ~ in(X2,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [X0] :
( X0 != empty_set
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f80,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f80]) ).
fof(f88,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) ) ) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f89,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,subset_complement(the_carrier(X0),X1))
<~> ~ in(X2,X1) ) ) ) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f91,plain,
! [X0] :
( empty_set = X0
| ! [X1] :
( ~ element(X1,powerset(X0))
| ! [X2] :
( ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(ennf_transformation,[],[f43]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(flattening,[],[f92]) ).
fof(f99,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) )
& ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) ) ) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f100,plain,
? [X0] :
( one_sorted_str(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ? [X2] :
( element(X2,the_carrier(X0))
& ( in(X2,subset_complement(the_carrier(X0),X1))
| ~ in(X2,X1) )
& ( ~ in(X2,subset_complement(the_carrier(X0),X1))
| in(X2,X1) ) ) ) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
( one_sorted_str(sK5)
& ~ empty_carrier(sK5)
& element(sK6,powerset(the_carrier(sK5)))
& element(sK7,the_carrier(sK5))
& ( in(sK7,subset_complement(the_carrier(sK5),sK6))
| ~ in(sK7,sK6) )
& ( ~ in(sK7,subset_complement(the_carrier(sK5),sK6))
| in(sK7,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f100]) ).
fof(f145,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f151,plain,
empty(empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f157,plain,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f158,plain,
~ empty_carrier(sK5),
inference(cnf_transformation,[],[f101]) ).
fof(f159,plain,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f101]) ).
fof(f160,plain,
element(sK7,the_carrier(sK5)),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
( in(sK7,subset_complement(the_carrier(sK5),sK6))
| ~ in(sK7,sK6) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
( ~ in(sK7,subset_complement(the_carrier(sK5),sK6))
| in(sK7,sK6) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
! [X2,X0,X1] :
( empty_set = X0
| ~ element(X1,powerset(X0))
| ~ element(X2,X0)
| in(X2,X1)
| in(X2,subset_complement(X0,X1)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2)) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_92,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_93,plain,
empty(empty_set),
inference(cnf_transformation,[],[f151]) ).
tcf(c_104,negated_conjecture,
( in(sK7,sK6)
| ~ in(sK7,subset_complement(the_carrier(sK5),sK6)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_105,negated_conjecture,
( in(sK7,subset_complement(the_carrier(sK5),sK6))
| ~ in(sK7,sK6) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_106,negated_conjecture,
element(sK7,the_carrier(sK5)),
inference(cnf_transformation,[],[f160]) ).
tcf(c_107,negated_conjecture,
element(sK6,powerset(the_carrier(sK5))),
inference(cnf_transformation,[],[f159]) ).
tcf(c_108,negated_conjecture,
~ empty_carrier(sK5),
inference(cnf_transformation,[],[f158]) ).
tcf(c_109,negated_conjecture,
one_sorted_str(sK5),
inference(cnf_transformation,[],[f157]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X0)
| in(X2,subset_complement(X1,X0))
| ( X1 = empty_set )
| ~ element(X2,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ element(X2,powerset(X1))
| ~ in(X0,subset_complement(X1,X2)) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_787,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_108]) ).
tcf(c_788,plain,
( ~ one_sorted_str(sK5)
| ~ empty(the_carrier(sK5)) ),
inference(unflattening,[status(thm)],[c_787]) ).
tcf(c_789,plain,
~ empty(the_carrier(sK5)),
inference(global_subsumption_just,[status(thm)],[c_788,c_109,c_788]) ).
tcf(c_1060,definition,
iPr_def_12 = powerset(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1061,definition,
iPr_def_13 = subset_complement(iPr_def_11,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1064,plain,
~ empty(iPr_def_11),
inference(demodulation,[status(thm)],[c_789]) ).
tcf(c_1065,negated_conjecture,
element(sK6,iPr_def_12),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_1066,negated_conjecture,
element(sK7,iPr_def_11),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_1067,negated_conjecture,
( in(sK7,iPr_def_13)
| ~ in(sK7,sK6) ),
inference(demodulation,[status(thm)],[c_105,c_1061]) ).
tcf(c_1068,negated_conjecture,
( in(sK7,sK6)
| ~ in(sK7,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_1822,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_13)
| ~ in(X0,sK6)
| ~ element(sK6,powerset(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1061,c_111]) ).
tcf(c_1823,plain,
! [X0: $i] :
( ~ element(sK6,iPr_def_12)
| ~ in(X0,iPr_def_13)
| ~ in(X0,sK6) ),
inference(light_normalisation,[status(thm)],[c_1822,c_1060]) ).
tcf(c_1824,plain,
! [X0: $i] :
( ~ in(X0,iPr_def_13)
| ~ in(X0,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1823,c_1065]) ).
tcf(c_1842,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| in(X0,sK6)
| ( empty_set = iPr_def_11 )
| ~ element(X0,iPr_def_11)
| ~ element(sK6,powerset(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_1061,c_110]) ).
tcf(c_1847,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| in(X0,sK6)
| ( empty_set = iPr_def_11 )
| ~ element(sK6,iPr_def_12)
| ~ element(X0,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_1842,c_1060]) ).
tcf(c_1848,plain,
! [X0: $i] :
( in(X0,iPr_def_13)
| in(X0,sK6)
| ( empty_set = iPr_def_11 )
| ~ element(X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1847,c_1065]) ).
tcf(c_1903,plain,
~ in(sK7,iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_1068,c_1824]) ).
tcf(c_1904,plain,
~ in(sK7,sK6),
inference(backward_subsumption_resolution,[status(thm)],[c_1067,c_1824]) ).
tcf(c_1917,plain,
( in(sK7,iPr_def_13)
| in(sK7,sK6)
| ( empty_set = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1066,c_1848]) ).
tcf(c_1918,plain,
empty_set = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1917,c_1903,c_1904]) ).
tcf(c_1921,plain,
empty(iPr_def_11),
inference(demodulation,[status(thm)],[c_93,c_1918]) ).
tcf(c_1922,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1921,c_1064]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU321+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:39:08 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.96/1.29 % SZS status Started for theBenchmark.p
% 1.96/1.29 % SZS status Theorem for theBenchmark.p
% 1.96/1.29
% 1.96/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.96/1.29
% 1.96/1.29 % ------ iProver source info
% 1.96/1.29
% 1.96/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.96/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.96/1.29 % git: non_committed_changes: false
% 1.96/1.29
% 1.96/1.29 % ------ Parsing...
% 1.96/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.96/1.29
% 1.96/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 40 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 1.96/1.29
% 1.96/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.96/1.29
% 1.96/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.96/1.29 % ------ Proving...
% 1.96/1.29 % ------ Problem Properties
% 1.96/1.29
% 1.96/1.29 %
% 1.96/1.29 % clauses 30
% 1.96/1.29 % conjectures 4
% 1.96/1.29 % EPR 15
% 1.96/1.29 % Horn 28
% 1.96/1.29 % unary 16
% 1.96/1.29 % binary 8
% 1.96/1.29 % lits 52
% 1.96/1.29 % lits eq 8
% 1.96/1.29 % fd_pure 0
% 1.96/1.29 % fd_pseudo 0
% 1.96/1.29 % fd_cond 2
% 1.96/1.29 % fd_pseudo_cond 1
% 1.96/1.29 % AC symbols 0
% 1.96/1.29
% 1.96/1.29 % ------ Schedule dynamic 5 is on
% 1.96/1.29
% 1.96/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.96/1.29
% 1.96/1.29
% 1.96/1.29 % ------
% 1.96/1.29 % Current options:
% 1.96/1.29 % ------
% 1.96/1.29
% 1.96/1.29
% 1.96/1.29 %
% 1.96/1.29
% 1.96/1.29 % ------ Proving...
% 1.96/1.29 %
% 1.96/1.29
% 1.96/1.29 % SZS status Theorem for theBenchmark.p
% 1.96/1.29
% 1.96/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.96/1.30
% 1.96/1.30
%------------------------------------------------------------------------------