%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET977+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 : n004.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 02:49:15 PM UTC 2026
% Result : Theorem 1.93s 1.27s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 19 unt; 3 def)
% Number of atoms : 153 ( 61 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 130 ( 59 ~; 49 |; 17 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 98 !; 4 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
<=> ( in(X1,X3)
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( X1 = X3
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(f11,conjecture,
! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(X0,singleton(X1)) != empty_set
& cartesian_product2(singleton(X1),X0) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_zfmisc_1) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( X0 != empty_set
=> ( cartesian_product2(X0,singleton(X1)) != empty_set
& cartesian_product2(singleton(X1),X0) != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
? [X0,X1] :
( X0 != empty_set
& ( empty_set = cartesian_product2(X0,singleton(X1))
| empty_set = cartesian_product2(singleton(X1),X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f15,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK0(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f16]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| ( in(X1,X3)
& X0 = X2 ) )
& ( ~ in(X1,X3)
| X0 != X2
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))
| ( in(X1,X3)
& X0 = X2 ) )
& ( ~ in(X1,X3)
| X0 != X2
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ( X1 = X3
& in(X0,X2) ) )
& ( X1 != X3
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ( X1 = X3
& in(X0,X2) ) )
& ( X1 != X3
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( empty_set != sK3
& ( empty_set = cartesian_product2(sK3,singleton(sK4))
| empty_set = cartesian_product2(singleton(sK4),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f14]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| X0 != X2
| in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
( empty_set = cartesian_product2(sK3,singleton(sK4))
| empty_set = cartesian_product2(singleton(sK4),sK3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| X0 != X2
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(singleton(X2),X3)) ),
inference(definition_unfolding,[],[f36,f29]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,singleton(X3))) ),
inference(definition_unfolding,[],[f39,f29]) ).
fof(f49,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f27]) ).
fof(f50,plain,
! [X2,X3,X1] :
( ~ in(X1,X3)
| in(unordered_pair(unordered_pair(X2,X1),singleton(X2)),cartesian_product2(singleton(X2),X3)) ),
inference(equality_resolution,[],[f43]) ).
fof(f51,plain,
! [X2,X3,X0] :
( ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X3),singleton(X0)),cartesian_product2(X2,singleton(X3))) ),
inference(equality_resolution,[],[f46]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f26]) ).
tcf(c_51,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f49]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(singleton(X2),X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),cartesian_product2(X1,singleton(X2)))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_63,negated_conjecture,
( ( cartesian_product2(sK3,singleton(sK4)) = empty_set )
| ( cartesian_product2(singleton(sK4),sK3) = empty_set ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_64,negated_conjecture,
empty_set != sK3,
inference(cnf_transformation,[],[f40]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X2)),cartesian_product2(X1,singleton(X2)))
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_60,c_50]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(singleton(X2),X1))
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_57,c_50]) ).
tcf(c_211,definition,
iPr_def_10 = singleton(sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_212,definition,
iPr_def_11 = cartesian_product2(iPr_def_10,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_213,definition,
iPr_def_12 = cartesian_product2(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_214,negated_conjecture,
empty_set != sK3,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_215,negated_conjecture,
( ( iPr_def_12 = empty_set )
| ( iPr_def_11 = empty_set ) ),
inference(demodulation,[status(thm)],[c_63,c_213,c_211,c_212]) ).
tcf(c_427,plain,
! [X0: $i] :
( ( empty_set = iPr_def_11 )
| ~ in(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_215,c_52]) ).
tcf(c_536,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),cartesian_product2(X1,iPr_def_10))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_211,c_141]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(sK4,X0)),cartesian_product2(iPr_def_10,X1))
| ~ in(X0,X1) ),
inference(superposition,[status(thm)],[c_211,c_155]) ).
tcf(c_780,plain,
! [X0: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(sK4,X0)),iPr_def_11)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_212,c_574]) ).
tcf(c_833,plain,
! [X0: $i] :
( in(unordered_pair(iPr_def_10,unordered_pair(X0,sK4)),iPr_def_11)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_50,c_780]) ).
tcf(c_1012,plain,
! [X0: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,sK4)),iPr_def_12)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_213,c_536]) ).
tcf(c_1051,plain,
! [X0: $i] :
( ( empty_set = iPr_def_11 )
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_1012,c_427]) ).
tcf(c_1074,plain,
( ( empty_set = iPr_def_11 )
| ( empty_set = sK3 ) ),
inference(superposition,[status(thm)],[c_51,c_1051]) ).
tcf(c_1075,plain,
empty_set = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1074,c_214]) ).
tcf(c_1087,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_51,c_1075]) ).
tcf(c_1088,plain,
! [X0: $i] : ~ in(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_52,c_1075]) ).
tcf(c_1091,plain,
sK3 != iPr_def_11,
inference(demodulation,[status(thm)],[c_214,c_1075]) ).
tcf(c_1092,plain,
! [X0: $i] : ~ in(X0,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_833,c_1088]) ).
tcf(c_1181,plain,
sK3 = iPr_def_11,
inference(superposition,[status(thm)],[c_1087,c_1092]) ).
tcf(c_1183,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1181,c_1091]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:29:52 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 1.93/1.27 % SZS status Started for theBenchmark.p
% 1.93/1.27 % SZS status Theorem for theBenchmark.p
% 1.93/1.27
% 1.93/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.93/1.27
% 1.93/1.27 % ------ iProver source info
% 1.93/1.27
% 1.93/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.93/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.93/1.27 % git: non_committed_changes: false
% 1.93/1.27
% 1.93/1.27 % ------ Parsing...
% 1.93/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... sup_sim: 7 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.93/1.27
% 1.93/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.93/1.27 % ------ Proving...
% 1.93/1.27 % ------ Problem Properties
% 1.93/1.27
% 1.93/1.27 %
% 1.93/1.27 % clauses 19
% 1.93/1.27 % conjectures 2
% 1.93/1.27 % EPR 7
% 1.93/1.27 % Horn 17
% 1.93/1.27 % unary 10
% 1.93/1.27 % binary 9
% 1.93/1.27 % lits 28
% 1.93/1.27 % lits eq 10
% 1.93/1.27 % fd_pure 0
% 1.93/1.27 % fd_pseudo 0
% 1.93/1.27 % fd_cond 1
% 1.93/1.27 % fd_pseudo_cond 2
% 1.93/1.27 % AC symbols 0
% 1.93/1.27
% 1.93/1.27 % ------ Schedule dynamic 5 is on
% 1.93/1.27
% 1.93/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.93/1.27
% 1.93/1.27
% 1.93/1.27 % ------
% 1.93/1.27 % Current options:
% 1.93/1.27 % ------
% 1.93/1.27
% 1.93/1.27
% 1.93/1.27 %
% 1.93/1.27
% 1.93/1.27 % ------ Proving...
% 1.93/1.27 %
% 1.93/1.27
% 1.93/1.27 % SZS status Theorem for theBenchmark.p
% 1.93/1.27
% 1.93/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.93/1.27
% 1.93/1.27
%------------------------------------------------------------------------------