%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:49:16 PM UTC 2026
% Result : Theorem 2.62s 6.49s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 19 unt; 4 def)
% Number of atoms : 170 ( 64 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 118 ( 43 ~; 58 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 57 !; 4 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f5,axiom,
! [X0,X1] :
( cartesian_product2(X0,X1) = empty_set
<=> ( X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
=> ( ( subset(X1,X3)
& subset(X0,X2) )
| cartesian_product2(X0,X1) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(f7,conjecture,
! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] :
( ~ empty(X0)
=> ! [X1,X2,X3] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
=> subset(X1,X3) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| ( subset(X1,X3)
& subset(X0,X2) )
| cartesian_product2(X0,X1) = empty_set ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| ( subset(X1,X3)
& subset(X0,X2) )
| cartesian_product2(X0,X1) = empty_set ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0] :
( ~ empty(X0)
& ? [X1,X2,X3] :
( ( subset(cartesian_product2(X1,X0),cartesian_product2(X3,X2))
| subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) )
& ~ subset(X1,X3) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f17,plain,
! [X0,X1] :
( ( empty_set != cartesian_product2(X0,X1)
| X1 = empty_set
| X0 = empty_set )
& ( ( empty_set != X1
& empty_set != X0 )
| cartesian_product2(X0,X1) = empty_set ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ~ empty(sK2)
& ( subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4))
| subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) )
& ~ subset(sK3,sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f13]) ).
fof(f19,plain,
empty(empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X1
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(X1,X3)
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3))
| subset(X0,X2)
| empty_set = cartesian_product2(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
~ empty(sK2),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
( subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4))
| subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
~ subset(sK3,sK5),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X1 = empty_set )
| ( X0 = empty_set )
| ( cartesian_product2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X0,X2)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(X1,X3)
| ( cartesian_product2(X0,X1) = empty_set )
| ~ subset(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_58,negated_conjecture,
~ subset(sK3,sK5),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,negated_conjecture,
( subset(cartesian_product2(sK2,sK3),cartesian_product2(sK4,sK5))
| subset(cartesian_product2(sK3,sK2),cartesian_product2(sK5,sK4)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,negated_conjecture,
~ empty(sK2),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,plain,
! [X0: $i] : subset(empty_set,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_135,plain,
empty_set != sK2,
inference(resolution_lifted,[status(thm)],[c_49,c_60]) ).
tcf(c_151,definition,
iPr_def_10 = cartesian_product2(sK3,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_152,definition,
iPr_def_11 = cartesian_product2(sK5,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_153,definition,
iPr_def_12 = cartesian_product2(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_154,definition,
iPr_def_13 = cartesian_product2(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_156,negated_conjecture,
( subset(iPr_def_12,iPr_def_13)
| subset(iPr_def_10,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_59,c_154,c_153,c_152,c_151]) ).
tcf(c_157,negated_conjecture,
~ subset(sK3,sK5),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_331,plain,
( ( empty_set = sK2 )
| ( empty_set = sK3 )
| ( empty_set != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_153,c_55]) ).
tcf(c_333,plain,
( ( empty_set = sK2 )
| ( empty_set = sK3 )
| ( empty_set != iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_151,c_55]) ).
tcf(c_347,plain,
( ( empty_set != iPr_def_12 )
| ( empty_set = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_331,c_135,c_331]) ).
tcf(c_348,plain,
( ( empty_set = sK3 )
| ( empty_set != iPr_def_12 ) ),
inference(renaming,[status(thm)],[c_347]) ).
tcf(c_359,plain,
( ( empty_set != iPr_def_10 )
| ( empty_set = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_333,c_135,c_333]) ).
tcf(c_360,plain,
( ( empty_set = sK3 )
| ( empty_set != iPr_def_10 ) ),
inference(renaming,[status(thm)],[c_359]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( subset(sK3,X0)
| ( cartesian_product2(sK3,sK2) = empty_set )
| ~ subset(iPr_def_10,cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_151,c_56]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] :
( subset(sK3,X0)
| ( empty_set = iPr_def_10 )
| ~ subset(iPr_def_10,cartesian_product2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_382,c_151]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i] :
( subset(sK3,X1)
| ( cartesian_product2(sK2,sK3) = empty_set )
| ~ subset(iPr_def_12,cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_153,c_57]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i] :
( subset(sK3,X1)
| ( empty_set = iPr_def_12 )
| ~ subset(iPr_def_12,cartesian_product2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_489,c_153]) ).
tcf(c_564,plain,
( subset(sK3,sK5)
| ( empty_set = iPr_def_10 )
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(superposition,[status(thm)],[c_152,c_412]) ).
tcf(c_565,plain,
( ( empty_set = iPr_def_10 )
| ~ subset(iPr_def_10,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_564,c_157]) ).
tcf(c_951,plain,
( subset(sK3,sK5)
| ( empty_set = iPr_def_12 )
| ~ subset(iPr_def_12,iPr_def_13) ),
inference(superposition,[status(thm)],[c_154,c_529]) ).
tcf(c_960,plain,
( ( empty_set = iPr_def_12 )
| ~ subset(iPr_def_12,iPr_def_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_951,c_157]) ).
tcf(c_978,plain,
( ( empty_set = sK2 )
| ( empty_set = sK3 )
| ( empty_set != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_153,c_55]) ).
tcf(c_998,plain,
( subset(iPr_def_10,iPr_def_11)
| ( empty_set = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_156,c_960]) ).
tcf(c_1005,plain,
( ( empty_set = iPr_def_12 )
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_998,c_565]) ).
tcf(c_1023,plain,
( ( empty_set = iPr_def_10 )
| ( empty_set = sK3 ) ),
inference(superposition,[status(thm)],[c_1005,c_348]) ).
tcf(c_1110,plain,
empty_set = sK3,
inference(global_subsumption_just,[status(thm)],[c_978,c_360,c_1023]) ).
tcf(c_1114,plain,
~ subset(empty_set,sK5),
inference(demodulation,[status(thm)],[c_157,c_1110]) ).
tcf(c_1115,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1114,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET985+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.40 % Computer : n001.cluster.edu
% 0.15/5.40 % Model : x86_64 x86_64
% 0.15/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.40 % Memory : 8046.5625MB
% 0.15/5.40 % OS : Linux 6.8.0-71-generic
% 0.15/5.40 % CPULimit : 300
% 0.15/5.40 % WCLimit : 300
% 0.15/5.40 % DateTime : Thu Sep 24 12:36:42 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.47 Running first-order theorem proving
% 0.15/5.47 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
% 0.15/5.49
% 0.15/5.49 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.49
% 0.15/5.49 % Detected problem language: tptp
% 0.19/5.51 % Proving...
% 2.62/6.49 % SZS status Started for theBenchmark.p
% 2.62/6.49 % SZS status Theorem for theBenchmark.p
% 2.62/6.49
% 2.62/6.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.62/6.49
% 2.62/6.49 % ------ iProver source info
% 2.62/6.49
% 2.62/6.49 % git: date: 2026-07-19 20:42:38 +0200
% 2.62/6.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.62/6.49 % git: non_committed_changes: false
% 2.62/6.49
% 2.62/6.49 % ------ Parsing...
% 2.62/6.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.62/6.49
% 2.62/6.49 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.62/6.49
% 2.62/6.49 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.62/6.49
% 2.62/6.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.62/6.49 % ------ Proving...
% 2.62/6.49 % ------ Problem Properties
% 2.62/6.49
% 2.62/6.49 %
% 2.62/6.49 % clauses 17
% 2.62/6.49 % conjectures 3
% 2.62/6.49 % EPR 8
% 2.62/6.49 % Horn 13
% 2.62/6.49 % unary 13
% 2.62/6.49 % binary 1
% 2.62/6.49 % lits 24
% 2.62/6.49 % lits eq 11
% 2.62/6.49 % fd_pure 0
% 2.62/6.49 % fd_pseudo 0
% 2.62/6.49 % fd_cond 1
% 2.62/6.49 % fd_pseudo_cond 0
% 2.62/6.49 % AC symbols 0
% 2.62/6.49
% 2.62/6.49 % ------ Schedule dynamic 5 is on
% 2.62/6.49
% 2.62/6.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.62/6.49
% 2.62/6.49
% 2.62/6.49 % ------
% 2.62/6.49 % Current options:
% 2.62/6.49 % ------
% 2.62/6.49
% 2.62/6.49
% 2.62/6.49 %
% 2.62/6.49
% 2.62/6.49 % ------ Proving...
% 2.62/6.49 %
% 2.62/6.49
% 2.62/6.49 % SZS status Theorem for theBenchmark.p
% 2.62/6.49
% 2.62/6.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.62/6.49
% 2.62/6.49
%------------------------------------------------------------------------------