%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 02:24:03 PM UTC 2026
% Result : Theorem 2.52s 1.42s
% Output : CNFRefutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 17 unt; 1 def)
% Number of atoms : 120 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 106 ( 50 ~; 42 |; 8 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 8 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 73 ( 0 sgn 71 !; 2 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f8,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f21,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f23,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f24,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f27,conjecture,
! [X0,X1] :
~ ( subset(X1,X0)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1] :
~ ( subset(X1,X0)
& in(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f31,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
? [X0,X1] :
( subset(X1,X0)
& in(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f65,plain,
( subset(sK12,sK11)
& in(sK11,sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f52]) ).
fof(f66,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f76,plain,
empty(empty_set),
inference(cnf_transformation,[],[f8]) ).
fof(f97,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f98,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f48]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f101,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f103,plain,
subset(sK12,sK11),
inference(cnf_transformation,[],[f65]) ).
fof(f104,plain,
in(sK11,sK12),
inference(cnf_transformation,[],[f65]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_56,plain,
empty(empty_set),
inference(cnf_transformation,[],[f76]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ empty(X1)
| ~ in(X2,X0)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_82,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ empty(X0) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_84,negated_conjecture,
in(sK11,sK12),
inference(cnf_transformation,[],[f104]) ).
tcf(c_85,negated_conjecture,
subset(sK12,sK11),
inference(cnf_transformation,[],[f103]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( element(X0,powerset(X1))
| ( X1 != sK11 )
| ( X0 != sK12 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_85]) ).
tcf(c_261,plain,
element(sK12,powerset(sK11)),
inference(unflattening,[status(thm)],[c_260]) ).
tcf(c_372,definition,
iPr_def_10 = powerset(sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_373,plain,
element(sK12,iPr_def_10),
inference(demodulation,[status(thm)],[c_261,c_372]) ).
tcf(c_374,negated_conjecture,
in(sK11,sK12),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] :
( element(X0,sK11)
| ~ element(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_372,c_80]) ).
tcf(c_801,plain,
( element(sK11,sK11)
| ~ element(sK12,iPr_def_10) ),
inference(superposition,[status(thm)],[c_374,c_667]) ).
tcf(c_806,plain,
element(sK11,sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_801,c_373]) ).
tcf(c_823,plain,
( empty(sK11)
| in(sK11,sK11) ),
inference(superposition,[status(thm)],[c_806,c_78]) ).
tcf(c_831,plain,
( empty(sK11)
| ~ in(sK11,sK11) ),
inference(superposition,[status(thm)],[c_823,c_49]) ).
tcf(c_836,plain,
empty(sK11),
inference(backward_subsumption_resolution,[status(thm)],[c_823,c_831]) ).
tcf(c_848,plain,
empty_set = sK11,
inference(superposition,[status(thm)],[c_836,c_82]) ).
tcf(c_859,plain,
powerset(empty_set) = iPr_def_10,
inference(demodulation,[status(thm)],[c_372,c_848]) ).
tcf(c_860,plain,
in(empty_set,sK12),
inference(demodulation,[status(thm)],[c_374,c_848]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i] :
( ~ empty(empty_set)
| ~ element(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_859,c_81]) ).
tcf(c_911,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,iPr_def_10)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_905,c_56]) ).
tcf(c_922,plain,
~ element(sK12,iPr_def_10),
inference(superposition,[status(thm)],[c_860,c_911]) ).
tcf(c_923,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_922,c_373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM383+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 03:49:17 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.54 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 2.52/1.42 % SZS status Started for theBenchmark.p
% 2.52/1.42 % SZS status Theorem for theBenchmark.p
% 2.52/1.42
% 2.52/1.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.52/1.42
% 2.52/1.42 % ------ iProver source info
% 2.52/1.42
% 2.52/1.42 % git: date: 2026-07-19 20:42:38 +0200
% 2.52/1.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.52/1.42 % git: non_committed_changes: false
% 2.52/1.42
% 2.52/1.42 % ------ Parsing...
% 2.52/1.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.52/1.42
% 2.52/1.42 % ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.52/1.42
% 2.52/1.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.52/1.42
% 2.52/1.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.52/1.42 % ------ Proving...
% 2.52/1.42 % ------ Problem Properties
% 2.52/1.42
% 2.52/1.42 %
% 2.52/1.42 % clauses 19
% 2.52/1.42 % conjectures 1
% 2.52/1.42 % EPR 14
% 2.52/1.42 % Horn 18
% 2.52/1.42 % unary 11
% 2.52/1.42 % binary 4
% 2.52/1.42 % lits 31
% 2.52/1.42 % lits eq 3
% 2.52/1.42 % fd_pure 0
% 2.52/1.42 % fd_pseudo 0
% 2.52/1.42 % fd_cond 1
% 2.52/1.42 % fd_pseudo_cond 1
% 2.52/1.42 % AC symbols 0
% 2.52/1.42
% 2.52/1.42 % ------ Schedule dynamic 5 is on
% 2.52/1.42
% 2.52/1.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.52/1.42
% 2.52/1.42
% 2.52/1.42 % ------
% 2.52/1.42 % Current options:
% 2.52/1.42 % ------
% 2.52/1.42
% 2.52/1.42
% 2.52/1.42 %
% 2.52/1.42
% 2.52/1.42 % ------ Proving...
% 2.52/1.42 %
% 2.52/1.42
% 2.52/1.42 % SZS status Theorem for theBenchmark.p
% 2.52/1.42
% 2.52/1.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.52/1.42
% 2.52/1.42
%------------------------------------------------------------------------------