%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU089+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 : n011.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 02:55:23 PM UTC 2026
% Result : Theorem 0.56s 6.29s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 19 unt; 2 def)
% Number of atoms : 70 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 23 ~; 13 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 22 !; 6 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(f51,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).
fof(f53,conjecture,
! [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(f54,negated_conjecture,
~ ! [X0,X1,X2] :
( ( finite(X2)
& finite(X1)
& finite(X0) )
=> finite(cartesian_product3(X0,X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f109,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(ennf_transformation,[],[f51]) ).
fof(f110,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(flattening,[],[f109]) ).
fof(f112,plain,
? [X0,X1,X2] :
( finite(X2)
& finite(X1)
& finite(X0)
& ~ finite(cartesian_product3(X0,X1,X2)) ),
inference(ennf_transformation,[],[f54]) ).
fof(f113,plain,
? [X0,X1,X2] :
( finite(X2)
& finite(X1)
& finite(X0)
& ~ finite(cartesian_product3(X0,X1,X2)) ),
inference(flattening,[],[f112]) ).
fof(f149,plain,
( finite(sK28)
& finite(sK27)
& finite(sK26)
& ~ finite(cartesian_product3(sK26,sK27,sK28)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27,sK28]),skolemize(X0,sK26),skolemize(X1,sK27),skolemize(X2,sK28)],[f113]) ).
fof(f173,plain,
! [X2,X0,X1] : cartesian_product3(X0,X1,X2) = cartesian_product2(cartesian_product2(X0,X1),X2),
inference(cnf_transformation,[],[f14]) ).
fof(f263,plain,
! [X0,X1] :
( ~ finite(X1)
| ~ finite(X0)
| finite(cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f265,plain,
finite(sK28),
inference(cnf_transformation,[],[f149]) ).
fof(f266,plain,
finite(sK27),
inference(cnf_transformation,[],[f149]) ).
fof(f267,plain,
finite(sK26),
inference(cnf_transformation,[],[f149]) ).
fof(f268,plain,
~ finite(cartesian_product3(sK26,sK27,sK28)),
inference(cnf_transformation,[],[f149]) ).
fof(f277,plain,
~ finite(cartesian_product2(cartesian_product2(sK26,sK27),sK28)),
inference(definition_unfolding,[],[f268,f173]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( finite(cartesian_product2(X1,X0))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_159,negated_conjecture,
~ finite(cartesian_product2(cartesian_product2(sK26,sK27),sK28)),
inference(cnf_transformation,[],[f277]) ).
tcf(c_160,negated_conjecture,
finite(sK26),
inference(cnf_transformation,[],[f267]) ).
tcf(c_161,negated_conjecture,
finite(sK27),
inference(cnf_transformation,[],[f266]) ).
tcf(c_162,negated_conjecture,
finite(sK28),
inference(cnf_transformation,[],[f265]) ).
tcf(c_917,definition,
iPr_def_10 = cartesian_product2(sK26,sK27),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_918,definition,
iPr_def_11 = cartesian_product2(iPr_def_10,sK28),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_919,negated_conjecture,
finite(sK28),
inference(demodulation,[status(thm)],[c_162]) ).
tcf(c_920,negated_conjecture,
finite(sK27),
inference(demodulation,[status(thm)],[c_161]) ).
tcf(c_921,negated_conjecture,
finite(sK26),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_922,negated_conjecture,
~ finite(iPr_def_11),
inference(demodulation,[status(thm)],[c_159,c_917,c_918]) ).
tcf(c_1452,plain,
( finite(iPr_def_10)
| ~ finite(sK27)
| ~ finite(sK26) ),
inference(superposition,[status(thm)],[c_917,c_157]) ).
tcf(c_1453,plain,
( finite(iPr_def_11)
| ~ finite(iPr_def_10)
| ~ finite(sK28) ),
inference(superposition,[status(thm)],[c_918,c_157]) ).
tcf(c_1454,plain,
~ finite(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1453,c_922,c_919]) ).
tcf(c_1455,plain,
( ~ finite(sK27)
| ~ finite(sK26) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1452,c_1454]) ).
tcf(c_1456,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1455,c_920,c_921]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU089+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n011.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 12:43:33 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 0.56/6.29 % SZS status Started for theBenchmark.p
% 0.56/6.29 % SZS status Theorem for theBenchmark.p
% 0.56/6.29
% 0.56/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.56/6.29
% 0.56/6.29 % ------ iProver source info
% 0.56/6.29
% 0.56/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.56/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.56/6.29 % git: non_committed_changes: false
% 0.56/6.29
% 0.56/6.29 % ------ Parsing...
% 0.56/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.56/6.29
% 0.56/6.29 % ------ 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 %
% 0.56/6.29
% 0.56/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.56/6.29
% 0.56/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.56/6.29 % ------ Proving...
% 0.56/6.29 % ------ Problem Properties
% 0.56/6.29
% 0.56/6.29 %
% 0.56/6.29 % clauses 48
% 0.56/6.29 % conjectures 4
% 0.56/6.29 % EPR 27
% 0.56/6.29 % Horn 42
% 0.56/6.29 % unary 30
% 0.56/6.29 % binary 10
% 0.56/6.29 % lits 75
% 0.56/6.29 % lits eq 4
% 0.56/6.29 % fd_pure 0
% 0.56/6.29 % fd_pseudo 0
% 0.56/6.29 % fd_cond 1
% 0.56/6.29 % fd_pseudo_cond 1
% 0.56/6.29 % AC symbols 0
% 0.56/6.29
% 0.56/6.29 % ------ Schedule dynamic 5 is on
% 0.56/6.29
% 0.56/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.56/6.29
% 0.56/6.29
% 0.56/6.29 % ------
% 0.56/6.29 % Current options:
% 0.56/6.29 % ------
% 0.56/6.29
% 0.56/6.29
% 0.56/6.29 %
% 0.56/6.29
% 0.56/6.29 % ------ Proving...
% 0.56/6.29 %
% 0.56/6.29
% 0.56/6.29 % SZS status Theorem for theBenchmark.p
% 0.56/6.29
% 0.56/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.56/6.29
% 0.56/6.29
%------------------------------------------------------------------------------