%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU090+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 : n026.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 02:55:24 PM UTC 2026
% Result : Theorem 2.16s 1.29s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 22 unt; 2 def)
% Number of atoms : 97 ( 4 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 25 |; 21 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 4 con; 0-4 aty)
% Number of variables : 49 ( 0 sgn 41 !; 8 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2,X3] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_zfmisc_1) ).
fof(f53,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f55,axiom,
! [X0,X1,X2] :
( ( finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product3(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).
fof(f56,conjecture,
! [X0,X1,X2,X3] :
( ( finite(X3)
& finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product4(X0,X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_finset_1) ).
fof(f57,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( finite(X3)
& finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product4(X0,X1,X2,X3)) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f116,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f117,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f116]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ finite(X2)
| ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product3(X0,X1,X2)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ~ finite(X2)
| ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product3(X0,X1,X2)) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
? [X0,X1,X2,X3] :
( finite(X3)
& finite(X2)
& finite(X1)
& finite(X0)
& ~ finite(cartesian_product4(X0,X1,X2,X3)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f122,plain,
? [X0,X1,X2,X3] :
( finite(X3)
& finite(X2)
& finite(X1)
& finite(X0)
& ~ finite(cartesian_product4(X0,X1,X2,X3)) ),
inference(flattening,[],[f121]) ).
fof(f158,plain,
( finite(sK29)
& finite(sK28)
& finite(sK27)
& finite(sK26)
& ~ finite(cartesian_product4(sK26,sK27,sK28,sK29)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27,sK28,sK29]),skolemize(X0,sK26),skolemize(X1,sK27),skolemize(X2,sK28),skolemize(X3,sK29)],[f122]) ).
fof(f182,plain,
! [X2,X3,X0,X1] : cartesian_product4(X0,X1,X2,X3) = cartesian_product2(cartesian_product3(X0,X1,X2),X3),
inference(cnf_transformation,[],[f14]) ).
fof(f274,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f276,plain,
! [X2,X0,X1] :
( ~ finite(X2)
| ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product3(X0,X1,X2)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f277,plain,
finite(sK29),
inference(cnf_transformation,[],[f158]) ).
fof(f278,plain,
finite(sK28),
inference(cnf_transformation,[],[f158]) ).
fof(f279,plain,
finite(sK27),
inference(cnf_transformation,[],[f158]) ).
fof(f280,plain,
finite(sK26),
inference(cnf_transformation,[],[f158]) ).
fof(f281,plain,
~ finite(cartesian_product4(sK26,sK27,sK28,sK29)),
inference(cnf_transformation,[],[f158]) ).
fof(f290,plain,
~ finite(cartesian_product2(cartesian_product3(sK26,sK27,sK28),sK29)),
inference(definition_unfolding,[],[f281,f182]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( finite(cartesian_product2(X1,X0))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i,X2: $i] :
( finite(cartesian_product3(X1,X0,X2))
| ~ finite(X2)
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_162,negated_conjecture,
~ finite(cartesian_product2(cartesian_product3(sK26,sK27,sK28),sK29)),
inference(cnf_transformation,[],[f290]) ).
tcf(c_163,negated_conjecture,
finite(sK26),
inference(cnf_transformation,[],[f280]) ).
tcf(c_164,negated_conjecture,
finite(sK27),
inference(cnf_transformation,[],[f279]) ).
tcf(c_165,negated_conjecture,
finite(sK28),
inference(cnf_transformation,[],[f278]) ).
tcf(c_166,negated_conjecture,
finite(sK29),
inference(cnf_transformation,[],[f277]) ).
tcf(c_1000,definition,
iPr_def_10 = cartesian_product3(sK26,sK27,sK28),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1001,definition,
iPr_def_11 = cartesian_product2(iPr_def_10,sK29),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1002,negated_conjecture,
finite(sK29),
inference(demodulation,[status(thm)],[c_166]) ).
tcf(c_1003,negated_conjecture,
finite(sK28),
inference(demodulation,[status(thm)],[c_165]) ).
tcf(c_1004,negated_conjecture,
finite(sK27),
inference(demodulation,[status(thm)],[c_164]) ).
tcf(c_1005,negated_conjecture,
finite(sK26),
inference(demodulation,[status(thm)],[c_163]) ).
tcf(c_1006,negated_conjecture,
~ finite(iPr_def_11),
inference(demodulation,[status(thm)],[c_162,c_1000,c_1001]) ).
tcf(c_1584,plain,
( finite(iPr_def_11)
| ~ finite(iPr_def_10)
| ~ finite(sK29) ),
inference(superposition,[status(thm)],[c_1001,c_159]) ).
tcf(c_1585,plain,
~ finite(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1584,c_1006,c_1002]) ).
tcf(c_1687,plain,
( finite(iPr_def_10)
| ~ finite(sK28)
| ~ finite(sK27)
| ~ finite(sK26) ),
inference(superposition,[status(thm)],[c_1000,c_161]) ).
tcf(c_1688,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1687,c_1585,c_1003,c_1004,c_1005]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU090+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 12:46:11 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.16/1.29 % SZS status Started for theBenchmark.p
% 2.16/1.29 % SZS status Theorem for theBenchmark.p
% 2.16/1.29
% 2.16/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.16/1.29
% 2.16/1.29 % ------ iProver source info
% 2.16/1.29
% 2.16/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.16/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.16/1.29 % git: non_committed_changes: false
% 2.16/1.29
% 2.16/1.29 % ------ Parsing...
% 2.16/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.16/1.29
% 2.16/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 70 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 2.16/1.29
% 2.16/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.16/1.29
% 2.16/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.16/1.29 % ------ Proving...
% 2.16/1.29 % ------ Problem Properties
% 2.16/1.29
% 2.16/1.29 %
% 2.16/1.29 % clauses 51
% 2.16/1.29 % conjectures 5
% 2.16/1.29 % EPR 28
% 2.16/1.29 % Horn 44
% 2.16/1.29 % unary 31
% 2.16/1.29 % binary 10
% 2.16/1.29 % lits 85
% 2.16/1.29 % lits eq 4
% 2.16/1.29 % fd_pure 0
% 2.16/1.29 % fd_pseudo 0
% 2.16/1.29 % fd_cond 1
% 2.16/1.29 % fd_pseudo_cond 1
% 2.16/1.29 % AC symbols 0
% 2.16/1.29
% 2.16/1.29 % ------ Schedule dynamic 5 is on
% 2.16/1.29
% 2.16/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.16/1.29
% 2.16/1.29
% 2.16/1.29 % ------
% 2.16/1.29 % Current options:
% 2.16/1.29 % ------
% 2.16/1.29
% 2.16/1.29
% 2.16/1.29 %
% 2.16/1.29
% 2.16/1.29 % ------ Proving...
% 2.16/1.29 %
% 2.16/1.29
% 2.16/1.29 % SZS status Theorem for theBenchmark.p
% 2.16/1.29
% 2.16/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.16/1.29
% 2.16/1.29
%------------------------------------------------------------------------------