%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:49:12 PM UTC 2026
% Result : Theorem 0.85s 1.19s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 27 unt; 2 def)
% Number of atoms : 171 ( 62 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 165 ( 74 ~; 65 |; 19 &)
% ( 3 <=>; 3 =>; 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 119 !; 8 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f10,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| X1 = empty_set
| X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t114_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
=> ( X0 = X1
| X1 = empty_set
| X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f14,plain,
? [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
& X0 != X1
& empty_set != X1
& empty_set != X0 ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
? [X0,X1] :
( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
& X0 != X1
& empty_set != X1
& empty_set != X0 ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,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,[],[f7]) ).
fof(f21,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,[],[f20]) ).
fof(f24,plain,
( cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3)
& sK3 != sK4
& empty_set != sK4
& empty_set != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1] :
( ( ( in(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1) )
& ( ~ in(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f25]) ).
fof(f28,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f29,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
empty_set != sK4,
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
empty_set != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| in(sK5(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X0)
| ~ in(sK5(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,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,[],[f36,f31]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f35,f31]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f34,f31]) ).
fof(f49,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f28]) ).
tcf(c_52,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f49]) ).
tcf(c_55,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,[],[f46]) ).
tcf(c_56,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,[],[f47]) ).
tcf(c_57,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,[],[f48]) ).
tcf(c_60,negated_conjecture,
empty_set != sK3,
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,negated_conjecture,
empty_set != sK4,
inference(cnf_transformation,[],[f41]) ).
tcf(c_62,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,negated_conjecture,
cartesian_product2(sK3,sK4) = cartesian_product2(sK4,sK3),
inference(cnf_transformation,[],[f39]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_140,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_57,c_50]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(X0,X2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3)) ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
tcf(c_160,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_55,c_50]) ).
tcf(c_201,definition,
iPr_def_10 = cartesian_product2(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_202,definition,
iPr_def_11 = cartesian_product2(sK4,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_203,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_63,c_202,c_201]) ).
tcf(c_204,negated_conjecture,
sK3 != sK4,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_205,negated_conjecture,
empty_set != sK4,
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_206,negated_conjecture,
empty_set != sK3,
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_403,plain,
cartesian_product2(sK4,sK3) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_202,c_203]) ).
tcf(c_429,plain,
! [X0: $i] :
( in(sK5(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_65,c_52]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( in(X1,sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_201,c_140]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_201,c_147]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK3)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_403,c_160]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3)
| ~ in(X1,sK3)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_539,c_512]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] :
( in(X1,sK4)
| ~ in(X1,sK3)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_539,c_474]) ).
tcf(c_644,plain,
! [X0: $i] :
( in(X0,sK3)
| ( empty_set = sK3 )
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_429,c_609]) ).
tcf(c_646,plain,
! [X0: $i] :
( in(X0,sK3)
| ~ in(X0,sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_644,c_206]) ).
tcf(c_658,plain,
! [X0: $i] :
( in(sK5(sK4,X0),sK3)
| in(sK5(sK4,X0),X0)
| ( X0 = sK4 ) ),
inference(superposition,[status(thm)],[c_65,c_646]) ).
tcf(c_720,plain,
( in(sK5(sK4,sK3),sK3)
| ( sK3 = sK4 ) ),
inference(equality_factoring,[status(thm)],[c_658]) ).
tcf(c_722,plain,
in(sK5(sK4,sK3),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_720,c_204]) ).
tcf(c_751,plain,
( ( sK3 = sK4 )
| ~ in(sK5(sK4,sK3),sK4) ),
inference(superposition,[status(thm)],[c_722,c_64]) ).
tcf(c_752,plain,
~ in(sK5(sK4,sK3),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_751,c_204]) ).
tcf(c_773,plain,
! [X0: $i] :
( in(sK5(sK4,sK3),sK4)
| ~ in(X0,sK4) ),
inference(superposition,[status(thm)],[c_722,c_610]) ).
tcf(c_776,plain,
! [X0: $i] : ~ in(X0,sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_773,c_752]) ).
tcf(c_786,plain,
empty_set = sK4,
inference(superposition,[status(thm)],[c_429,c_776]) ).
tcf(c_790,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_786,c_205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET961+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 12:27:56 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 0.85/1.19 % SZS status Started for theBenchmark.p
% 0.85/1.19 % SZS status Theorem for theBenchmark.p
% 0.85/1.19
% 0.85/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/1.19
% 0.85/1.19 % ------ iProver source info
% 0.85/1.19
% 0.85/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/1.19 % git: non_committed_changes: false
% 0.85/1.19
% 0.85/1.19 % ------ Parsing...
% 0.85/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.85/1.19
% 0.85/1.19 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.85/1.19
% 0.85/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.85/1.19
% 0.85/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.85/1.19 % ------ Proving...
% 0.85/1.19 % ------ Problem Properties
% 0.85/1.19
% 0.85/1.19 %
% 0.85/1.19 % clauses 19
% 0.85/1.19 % conjectures 4
% 0.85/1.19 % EPR 9
% 0.85/1.19 % Horn 17
% 0.85/1.19 % unary 12
% 0.85/1.19 % binary 4
% 0.85/1.19 % lits 29
% 0.85/1.19 % lits eq 10
% 0.85/1.19 % fd_pure 0
% 0.85/1.19 % fd_pseudo 0
% 0.85/1.19 % fd_cond 1
% 0.85/1.19 % fd_pseudo_cond 2
% 0.85/1.19 % AC symbols 0
% 0.85/1.19
% 0.85/1.19 % ------ Schedule dynamic 5 is on
% 0.85/1.19
% 0.85/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.85/1.19
% 0.85/1.19
% 0.85/1.19 % ------
% 0.85/1.19 % Current options:
% 0.85/1.19 % ------
% 0.85/1.19
% 0.85/1.19
% 0.85/1.19 %
% 0.85/1.19
% 0.85/1.19 % ------ Proving...
% 0.85/1.19 %
% 0.85/1.19
% 0.85/1.19 % SZS status Theorem for theBenchmark.p
% 0.85/1.19
% 0.85/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/1.19
% 0.85/1.19
%------------------------------------------------------------------------------