%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 02:49:12 PM UTC 2026
% Result : Theorem 0.93s 1.29s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 17 unt; 2 def)
% Number of atoms : 127 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 44 ~; 49 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 1 <~>)
% 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 90 !; 4 ?; 37 :)
% 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] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f5,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(f8,conjecture,
! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t115_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f12,plain,
? [X0,X1] :
( cartesian_product2(X0,X0) = cartesian_product2(X1,X1)
& X0 != X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
<~> in(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,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,[],[f5]) ).
fof(f15,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,[],[f14]) ).
fof(f18,plain,
( cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3)
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( in(X2,X0)
| in(X2,X1) )
& ( ~ in(X2,X0)
| ~ in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( ( ( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1) )
& ( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f19]) ).
fof(f22,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f23,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f3]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| in(sK4(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X0)
| ~ in(sK4(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,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,[],[f27,f23]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f26,f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_52,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,[],[f35]) ).
tcf(c_53,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,[],[f36]) ).
tcf(c_57,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,negated_conjecture,
cartesian_product2(sK2,sK2) = cartesian_product2(sK3,sK3),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_125,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_53,c_50]) ).
tcf(c_138,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_52,c_50]) ).
tcf(c_168,definition,
iPr_def_10 = cartesian_product2(sK2,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_169,definition,
iPr_def_11 = cartesian_product2(sK3,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_170,negated_conjecture,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_58,c_169,c_168]) ).
tcf(c_171,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_344,plain,
cartesian_product2(sK3,sK3) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_169,c_170]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( in(X0,sK2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_168,c_125]) ).
tcf(c_388,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_344,c_125]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i] :
( in(X0,sK2)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_387]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] :
( in(X0,sK3)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_50,c_388]) ).
tcf(c_491,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK2)
| ~ in(X0,sK2) ),
inference(superposition,[status(thm)],[c_168,c_138]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),iPr_def_10)
| ~ in(X1,sK3)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_344,c_138]) ).
tcf(c_532,plain,
! [X0: $i] :
( in(X0,sK3)
| ~ in(X0,sK2) ),
inference(superposition,[status(thm)],[c_491,c_433]) ).
tcf(c_550,plain,
( ( sK2 = sK3 )
| ~ in(sK4(sK2,sK3),sK3)
| ~ in(sK4(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_564,plain,
! [X0: $i] :
( in(X0,sK2)
| ~ in(X0,sK3) ),
inference(superposition,[status(thm)],[c_492,c_425]) ).
tcf(c_636,plain,
! [X0: $i] :
( in(sK4(X0,sK3),sK2)
| in(sK4(X0,sK3),X0)
| ( X0 = sK3 ) ),
inference(superposition,[status(thm)],[c_60,c_564]) ).
tcf(c_645,plain,
( in(sK4(sK2,sK3),sK2)
| ( sK2 = sK3 ) ),
inference(instantiation,[status(thm)],[c_636]) ).
tcf(c_693,plain,
( in(sK4(sK2,sK3),sK2)
| ( sK2 = sK3 ) ),
inference(equality_factoring,[status(thm)],[c_636]) ).
tcf(c_695,plain,
in(sK4(sK2,sK3),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_693,c_171]) ).
tcf(c_713,plain,
in(sK4(sK2,sK3),sK3),
inference(superposition,[status(thm)],[c_695,c_532]) ).
tcf(c_714,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_713,c_645,c_550,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET962+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:28:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.93/1.29 % SZS status Started for theBenchmark.p
% 0.93/1.29 % SZS status Theorem for theBenchmark.p
% 0.93/1.29
% 0.93/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.93/1.29
% 0.93/1.29 % ------ iProver source info
% 0.93/1.29
% 0.93/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.93/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.93/1.29 % git: non_committed_changes: false
% 0.93/1.29
% 0.93/1.29 % ------ Parsing...
% 0.93/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.93/1.29
% 0.93/1.29 % ------ Preprocessing... sup_sim: 4 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.93/1.29
% 0.93/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.93/1.29
% 0.93/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.93/1.29 % ------ Proving...
% 0.93/1.29 % ------ Problem Properties
% 0.93/1.29
% 0.93/1.29 %
% 0.93/1.29 % clauses 14
% 0.93/1.29 % conjectures 2
% 0.93/1.29 % EPR 5
% 0.93/1.29 % Horn 13
% 0.93/1.29 % unary 8
% 0.93/1.29 % binary 3
% 0.93/1.29 % lits 23
% 0.93/1.29 % lits eq 7
% 0.93/1.29 % fd_pure 0
% 0.93/1.29 % fd_pseudo 0
% 0.93/1.29 % fd_cond 0
% 0.93/1.29 % fd_pseudo_cond 2
% 0.93/1.29 % AC symbols 0
% 0.93/1.29
% 0.93/1.29 % ------ Schedule dynamic 5 is on
% 0.93/1.29
% 0.93/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.93/1.29
% 0.93/1.29
% 0.93/1.29 % ------
% 0.93/1.29 % Current options:
% 0.93/1.29 % ------
% 0.93/1.29
% 0.93/1.29
% 0.93/1.29 %
% 0.93/1.29
% 0.93/1.29 % ------ Proving...
% 0.93/1.29 %
% 0.93/1.29
% 0.93/1.29 % SZS status Theorem for theBenchmark.p
% 0.93/1.29
% 0.93/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.93/1.29
% 0.93/1.29
%------------------------------------------------------------------------------