%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET950+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 : n014.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 02:49:11 PM UTC 2026
% Result : Theorem 2.76s 1.27s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 17 unt; 1 def)
% Number of atoms : 174 ( 48 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 204 ( 89 ~; 74 |; 35 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 122 !; 16 ?; 29 :)
% 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,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f5,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(f10,conjecture,
! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( X3 = ordered_pair(X4,X5)
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t103_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( ! [X4,X5] :
~ ( X3 = ordered_pair(X4,X5)
& in(X5,X2)
& in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f15,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X2)
| ~ in(X4,X1) )
& in(X3,X0)
& subset(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X4,X5] :
( X3 = ordered_pair(X4,X5)
& in(X5,X1)
& in(X4,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) != X2
| ! [X8] :
( ( ~ in(X8,X2)
| ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) )
& ( ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) )
| in(X8,X2) ) ) )
& ( ( ( in(sK0(X0,X1,X2),X2)
| ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) )
& ( ~ in(sK0(X0,X1,X2),X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) ) ) )
| X2 = cartesian_product2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X6,sK1(X0,X1,X2)),skolemize(X7,sK2(X0,X1,X2)),skolemize(X11,sK3(X0,X1,X8)),skolemize(X12,sK4(X0,X1,X8))],[f18]) ).
fof(f22,plain,
( ! [X4,X5] :
( ordered_pair(X4,X5) != sK10
| ~ in(X5,sK9)
| ~ in(X4,sK8) )
& in(sK10,sK7)
& subset(sK7,cartesian_product2(sK8,sK9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10)],[f16]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK4(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| in(sK3(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X4,X5] :
( ordered_pair(X4,X5) != sK10
| ~ in(X5,sK9)
| ~ in(X4,sK8) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
in(sK10,sK7),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
subset(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f22]) ).
fof(f45,plain,
! [X2,X0,X1,X8] :
( cartesian_product2(X0,X1) != X2
| ~ in(X8,X2)
| unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
inference(definition_unfolding,[],[f25,f34]) ).
fof(f47,plain,
! [X4,X5] :
( sK10 != unordered_pair(unordered_pair(X4,X5),singleton(X4))
| ~ in(X5,sK9)
| ~ in(X4,sK8) ),
inference(definition_unfolding,[],[f39,f34]) ).
fof(f50,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK3(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f27]) ).
fof(f51,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK4(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f26]) ).
fof(f52,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8 ),
inference(equality_resolution,[],[f45]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK3(X1,X2,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK4(X1,X2,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_64,negated_conjecture,
subset(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,negated_conjecture,
in(sK10,sK7),
inference(cnf_transformation,[],[f40]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ in(X1,sK9)
| ~ in(X0,sK8)
| ( unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK10 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK9)
| ~ in(X0,sK8)
| ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK10 ) ),
inference(demodulation,[status(thm)],[c_66,c_50]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 )
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(demodulation,[status(thm)],[c_58,c_50]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,X1)
| ~ in(X2,X0)
| ( X0 != sK7 )
| ( cartesian_product2(sK8,sK9) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_64]) ).
tcf(c_263,plain,
! [X0: $i] :
( in(X0,cartesian_product2(sK8,sK9))
| ~ in(X0,sK7) ),
inference(unflattening,[status(thm)],[c_262]) ).
tcf(c_419,definition,
iPr_def_10 = cartesian_product2(sK8,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_420,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ in(X0,sK7) ),
inference(demodulation,[status(thm)],[c_263,c_419]) ).
tcf(c_421,plain,
! [X0: $i,X1: $i] :
( ~ in(X1,sK9)
| ~ in(X0,sK8)
| ( unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK10 ) ),
inference(demodulation,[status(thm)],[c_171]) ).
tcf(c_422,negated_conjecture,
in(sK10,sK7),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_660,plain,
in(sK10,iPr_def_10),
inference(superposition,[status(thm)],[c_422,c_420]) ).
tcf(c_804,plain,
! [X0: $i] :
( ( unordered_pair(singleton(sK3(sK8,sK9,X0)),unordered_pair(sK3(sK8,sK9,X0),sK4(sK8,sK9,X0))) = X0 )
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_419,c_203]) ).
tcf(c_1652,plain,
unordered_pair(singleton(sK3(sK8,sK9,sK10)),unordered_pair(sK3(sK8,sK9,sK10),sK4(sK8,sK9,sK10))) = sK10,
inference(superposition,[status(thm)],[c_660,c_804]) ).
tcf(c_1919,plain,
( ~ in(sK4(sK8,sK9,sK10),sK9)
| ~ in(sK3(sK8,sK9,sK10),sK8) ),
inference(superposition,[status(thm)],[c_1652,c_421]) ).
tcf(c_2038,plain,
( ~ in(sK10,cartesian_product2(sK8,sK9))
| ~ in(sK4(sK8,sK9,sK10),sK9) ),
inference(superposition,[status(thm)],[c_56,c_1919]) ).
tcf(c_2039,plain,
( ~ in(sK10,iPr_def_10)
| ~ in(sK4(sK8,sK9,sK10),sK9) ),
inference(light_normalisation,[status(thm)],[c_2038,c_419]) ).
tcf(c_2040,plain,
~ in(sK4(sK8,sK9,sK10),sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2039,c_660]) ).
tcf(c_2041,plain,
~ in(sK10,cartesian_product2(sK8,sK9)),
inference(superposition,[status(thm)],[c_57,c_2040]) ).
tcf(c_2042,plain,
~ in(sK10,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_2041,c_419]) ).
tcf(c_2043,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2042,c_660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET950+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 : n014.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:26:17 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 2.76/1.27 % SZS status Started for theBenchmark.p
% 2.76/1.27 % SZS status Theorem for theBenchmark.p
% 2.76/1.27
% 2.76/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.76/1.27
% 2.76/1.27 % ------ iProver source info
% 2.76/1.27
% 2.76/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.76/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.76/1.27 % git: non_committed_changes: false
% 2.76/1.27
% 2.76/1.27 % ------ Parsing...
% 2.76/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.76/1.27
% 2.76/1.27 % ------ Preprocessing... sup_sim: 6 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 %
% 2.76/1.27
% 2.76/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.76/1.27
% 2.76/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.76/1.27 % ------ Proving...
% 2.76/1.27 % ------ Problem Properties
% 2.76/1.27
% 2.76/1.27 %
% 2.76/1.27 % clauses 17
% 2.76/1.27 % conjectures 1
% 2.76/1.27 % EPR 5
% 2.76/1.27 % Horn 14
% 2.76/1.27 % unary 6
% 2.76/1.27 % binary 5
% 2.76/1.27 % lits 36
% 2.76/1.27 % lits eq 10
% 2.76/1.27 % fd_pure 0
% 2.76/1.27 % fd_pseudo 0
% 2.76/1.27 % fd_cond 0
% 2.76/1.27 % fd_pseudo_cond 4
% 2.76/1.27 % AC symbols 0
% 2.76/1.27
% 2.76/1.27 % ------ Schedule dynamic 5 is on
% 2.76/1.27
% 2.76/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.76/1.27
% 2.76/1.27
% 2.76/1.27 % ------
% 2.76/1.27 % Current options:
% 2.76/1.27 % ------
% 2.76/1.27
% 2.76/1.27
% 2.76/1.27 %
% 2.76/1.27
% 2.76/1.27 % ------ Proving...
% 2.76/1.27 %
% 2.76/1.27
% 2.76/1.27 % SZS status Theorem for theBenchmark.p
% 2.76/1.27
% 2.76/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.76/1.27
% 2.76/1.27
%------------------------------------------------------------------------------