%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET949+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 : n019.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 1.86s 1.26s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 16 unt; 1 def)
% Number of atoms : 100 ( 44 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 114 ( 47 ~; 38 |; 27 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 95 ( 0 sgn 80 !; 15 ?; 15 :)
% 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] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f8,conjecture,
! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f17,plain,
( ! [X3,X4] : ordered_pair(X3,X4) != sK7
& in(sK7,cartesian_product2(sK8,sK9)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9)],[f11]) ).
fof(f19,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f20,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,[],[f14]) ).
fof(f28,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f32,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK7,
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
in(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f17]) ).
fof(f37,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,[],[f20,f28]) ).
fof(f39,plain,
! [X3,X4] : sK7 != unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(definition_unfolding,[],[f32,f28]) ).
fof(f44,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,[],[f37]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f19]) ).
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,[],[f44]) ).
tcf(c_62,negated_conjecture,
in(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_63,negated_conjecture,
! [X0: $i,X1: $i] : unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK7,
inference(cnf_transformation,[],[f39]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] : unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK7,
inference(demodulation,[status(thm)],[c_63,c_50]) ).
tcf(c_170,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_226,definition,
iPr_def_10 = cartesian_product2(sK8,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] : unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK7,
inference(demodulation,[status(thm)],[c_139]) ).
tcf(c_228,negated_conjecture,
in(sK7,iPr_def_10),
inference(demodulation,[status(thm)],[c_62,c_226]) ).
tcf(c_609,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_226,c_170]) ).
tcf(c_734,plain,
unordered_pair(singleton(sK3(sK8,sK9,sK7)),unordered_pair(sK3(sK8,sK9,sK7),sK4(sK8,sK9,sK7))) = sK7,
inference(superposition,[status(thm)],[c_228,c_609]) ).
tcf(c_737,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_734,c_227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET949+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 : n019.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 12:25:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.86/1.26 % SZS status Started for theBenchmark.p
% 1.86/1.26 % SZS status Theorem for theBenchmark.p
% 1.86/1.26
% 1.86/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.86/1.26
% 1.86/1.26 % ------ iProver source info
% 1.86/1.26
% 1.86/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 1.86/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.86/1.26 % git: non_committed_changes: false
% 1.86/1.26
% 1.86/1.26 % ------ Parsing...
% 1.86/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.86/1.26
% 1.86/1.26 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.86/1.26
% 1.86/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.86/1.26
% 1.86/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.86/1.26 % ------ Proving...
% 1.86/1.26 % ------ Problem Properties
% 1.86/1.26
% 1.86/1.26 %
% 1.86/1.26 % clauses 16
% 1.86/1.26 % conjectures 1
% 1.86/1.26 % EPR 4
% 1.86/1.26 % Horn 13
% 1.86/1.26 % unary 7
% 1.86/1.26 % binary 4
% 1.86/1.26 % lits 32
% 1.86/1.26 % lits eq 10
% 1.86/1.26 % fd_pure 0
% 1.86/1.26 % fd_pseudo 0
% 1.86/1.26 % fd_cond 0
% 1.86/1.26 % fd_pseudo_cond 4
% 1.86/1.26 % AC symbols 0
% 1.86/1.26
% 1.86/1.26 % ------ Schedule dynamic 5 is on
% 1.86/1.26
% 1.86/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.86/1.26
% 1.86/1.26
% 1.86/1.26 % ------
% 1.86/1.26 % Current options:
% 1.86/1.26 % ------
% 1.86/1.26
% 1.86/1.26
% 1.86/1.26 %
% 1.86/1.26
% 1.86/1.26 % ------ Proving...
% 1.86/1.26 %
% 1.86/1.26
% 1.86/1.26 % SZS status Theorem for theBenchmark.p
% 1.86/1.26
% 1.86/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.86/1.26
% 1.86/1.26
%------------------------------------------------------------------------------