%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET976+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 : n003.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 0.86s 1.18s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 19 unt; 5 def)
% Number of atoms : 214 ( 61 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 194 ( 81 ~; 84 |; 23 &)
% ( 5 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 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 : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 123 ( 0 sgn 109 !; 14 ?; 34 :)
% 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] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
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(f6,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f9,conjecture,
! [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(f10,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<=> ( X1 = X3
& in(X0,X2) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
<~> ( X1 = X3
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ( in(X1,X3)
& in(X0,X2) ) )
& ( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f16]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ( X1 = X3
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| X1 != X3
| ~ in(X0,X2) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f21,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| ( X1 = X3
& in(X0,X2) ) )
& ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))
| X1 != X3
| ~ in(X0,X2) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
( ( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 = sK6
& in(sK3,sK5) ) )
& ( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| sK4 != sK6
| ~ in(sK3,sK5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f21]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f25,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| ~ in(X3,X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| sK4 = sK6 ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
( in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| in(sK3,sK5) ),
inference(cnf_transformation,[],[f22]) ).
fof(f38,plain,
( ~ in(ordered_pair(sK3,sK4),cartesian_product2(sK5,singleton(sK6)))
| sK4 != sK6
| ~ in(sK3,sK5) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f33,f29]) ).
fof(f41,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f32,f29]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f31,f29]) ).
fof(f43,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| sK4 != sK6
| ~ in(sK3,sK5) ),
inference(definition_unfolding,[],[f38,f29]) ).
fof(f44,plain,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| in(sK3,sK5) ),
inference(definition_unfolding,[],[f37,f29]) ).
fof(f45,plain,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| sK4 = sK6 ),
inference(definition_unfolding,[],[f36,f29]) ).
fof(f46,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f26]) ).
fof(f47,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f46]) ).
fof(f48,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,negated_conjecture,
( ~ in(sK3,sK5)
| ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 != sK6 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_62,negated_conjecture,
( in(sK3,sK5)
| in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6))) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,negated_conjecture,
( in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 = sK6 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_93,plain,
in(sK3,sK5),
inference(backward_subsumption_resolution,[status(thm)],[c_62,c_57]) ).
tcf(c_95,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK4),singleton(sK3)),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 != sK6 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_61,c_57]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X1,X3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_58,c_50]) ).
tcf(c_149,plain,
( in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 = sK6 ) ),
inference(demodulation,[status(thm)],[c_63,c_50]) ).
tcf(c_162,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK4)),cartesian_product2(sK5,singleton(sK6)))
| ( sK4 != sK6 ) ),
inference(demodulation,[status(thm)],[c_95,c_50]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X0)),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
tcf(c_206,definition,
iPr_def_10 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_207,definition,
iPr_def_11 = unordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_208,definition,
iPr_def_12 = unordered_pair(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_209,definition,
iPr_def_13 = singleton(sK6),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_210,definition,
iPr_def_14 = cartesian_product2(sK5,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_211,plain,
( ~ in(iPr_def_12,iPr_def_14)
| ( sK4 != sK6 ) ),
inference(demodulation,[status(thm)],[c_162,c_209,c_210,c_207,c_206,c_208]) ).
tcf(c_212,plain,
( in(iPr_def_12,iPr_def_14)
| ( sK4 = sK6 ) ),
inference(demodulation,[status(thm)],[c_149]) ).
tcf(c_213,plain,
in(sK3,sK5),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_572,plain,
in(sK6,iPr_def_13),
inference(superposition,[status(thm)],[c_209,c_53]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i] :
( in(sK4,X1)
| ~ in(unordered_pair(singleton(sK3),iPr_def_11),cartesian_product2(X0,X1)) ),
inference(superposition,[status(thm)],[c_207,c_135]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( in(sK4,X1)
| ~ in(iPr_def_12,cartesian_product2(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_616,c_206,c_208]) ).
tcf(c_643,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ in(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_209,c_54]) ).
tcf(c_744,plain,
( in(sK4,iPr_def_13)
| ~ in(iPr_def_12,iPr_def_14) ),
inference(superposition,[status(thm)],[c_210,c_623]) ).
tcf(c_751,plain,
( in(sK4,iPr_def_13)
| ( sK4 = sK6 ) ),
inference(superposition,[status(thm)],[c_212,c_744]) ).
tcf(c_756,plain,
sK4 = sK6,
inference(forward_subsumption_resolution,[status(thm)],[c_751,c_643]) ).
tcf(c_762,plain,
in(sK4,iPr_def_13),
inference(demodulation,[status(thm)],[c_572,c_756]) ).
tcf(c_764,plain,
( ~ in(iPr_def_12,iPr_def_14)
| ( sK4 != sK4 ) ),
inference(demodulation,[status(thm)],[c_211,c_756]) ).
tcf(c_767,plain,
~ in(iPr_def_12,iPr_def_14),
inference(equality_resolution_simp,[status(thm)],[c_764]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(sK3),iPr_def_11),cartesian_product2(X0,X1))
| ~ in(sK4,X1)
| ~ in(sK3,X0) ),
inference(superposition,[status(thm)],[c_207,c_169]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i] :
( in(iPr_def_12,cartesian_product2(X0,X1))
| ~ in(sK4,X1)
| ~ in(sK3,X0) ),
inference(light_normalisation,[status(thm)],[c_824,c_206,c_208]) ).
tcf(c_1503,plain,
( in(iPr_def_12,iPr_def_14)
| ~ in(sK4,iPr_def_13)
| ~ in(sK3,sK5) ),
inference(superposition,[status(thm)],[c_210,c_836]) ).
tcf(c_1507,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1503,c_767,c_762,c_213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET976+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n003.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:30:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.86/1.18 % SZS status Started for theBenchmark.p
% 0.86/1.18 % SZS status Theorem for theBenchmark.p
% 0.86/1.18
% 0.86/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.86/1.18
% 0.86/1.18 % ------ iProver source info
% 0.86/1.18
% 0.86/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 0.86/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.86/1.18 % git: non_committed_changes: false
% 0.86/1.18
% 0.86/1.18 % ------ Parsing...
% 0.86/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.86/1.18
% 0.86/1.18 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.86/1.18
% 0.86/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.86/1.18
% 0.86/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.86/1.18 % ------ Proving...
% 0.86/1.18 % ------ Problem Properties
% 0.86/1.18
% 0.86/1.18 %
% 0.86/1.18 % clauses 20
% 0.86/1.18 % conjectures 0
% 0.86/1.18 % EPR 6
% 0.86/1.18 % Horn 18
% 0.86/1.18 % unary 11
% 0.86/1.18 % binary 6
% 0.86/1.18 % lits 32
% 0.86/1.18 % lits eq 13
% 0.86/1.18 % fd_pure 0
% 0.86/1.18 % fd_pseudo 0
% 0.86/1.18 % fd_cond 0
% 0.86/1.18 % fd_pseudo_cond 2
% 0.86/1.18 % AC symbols 0
% 0.86/1.18
% 0.86/1.18 % ------ Schedule dynamic 5 is on
% 0.86/1.18
% 0.86/1.18 % ------ no conjectures: strip conj schedule
% 0.86/1.18
% 0.86/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.86/1.18
% 0.86/1.18
% 0.86/1.18 % ------
% 0.86/1.18 % Current options:
% 0.86/1.18 % ------
% 0.86/1.18
% 0.86/1.18
% 0.86/1.18 %
% 0.86/1.18
% 0.86/1.18 % ------ Proving...
% 0.86/1.18 %
% 0.86/1.18
% 0.86/1.18 % SZS status Theorem for theBenchmark.p
% 0.86/1.18
% 0.86/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.86/1.18
%------------------------------------------------------------------------------