%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET978+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 : n004.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 02:49:15 PM UTC 2026
% Result : Theorem 0.43s 11.29s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 13 unt; 6 def)
% Number of atoms : 100 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 59 ( 30 ~; 20 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 45 !; 4 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
=> disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(f5,conjecture,
! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1)))
& disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( X0 != X1
=> ( disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1)))
& disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3)) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 != X1
=> disjoint(singleton(X0),singleton(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( ~ disjoint(X2,X3)
& ~ disjoint(X0,X1) )
| disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0,X1,X2,X3] :
( X0 != X1
& ( ~ disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1)))
| ~ disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( X0 = X1
| disjoint(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f7]) ).
fof(f14,plain,
( sK2 != sK3
& ( ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3)))
| ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f10]) ).
fof(f18,plain,
! [X2,X3,X0,X1] :
( ~ disjoint(X2,X3)
| disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f19,plain,
! [X2,X3,X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f20,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
( ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3)))
| ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( X0 = X1
| disjoint(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( disjoint(cartesian_product2(X2,X0),cartesian_product2(X3,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,negated_conjecture,
( ~ disjoint(cartesian_product2(sK4,singleton(sK2)),cartesian_product2(sK5,singleton(sK3)))
| ~ disjoint(cartesian_product2(singleton(sK2),sK4),cartesian_product2(singleton(sK3),sK5)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_55,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f20]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( disjoint(singleton(X0),singleton(X1))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_163,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_164,definition,
iPr_def_11 = cartesian_product2(iPr_def_10,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_165,definition,
iPr_def_12 = singleton(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_166,definition,
iPr_def_13 = cartesian_product2(iPr_def_12,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_167,definition,
iPr_def_14 = cartesian_product2(sK4,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_168,definition,
iPr_def_15 = cartesian_product2(sK5,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_169,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_170,negated_conjecture,
( ~ disjoint(iPr_def_14,iPr_def_15)
| ~ disjoint(iPr_def_11,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_54,c_168,c_167,c_165,c_166,c_163,c_164]) ).
tcf(c_317,plain,
! [X0: $i] :
( disjoint(iPr_def_10,singleton(X0))
| ( X0 = sK2 ) ),
inference(superposition,[status(thm)],[c_163,c_56]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( disjoint(iPr_def_11,cartesian_product2(X0,X1))
| ~ disjoint(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_164,c_52]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] :
( disjoint(iPr_def_14,cartesian_product2(X1,X0))
| ~ disjoint(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_167,c_53]) ).
tcf(c_423,plain,
( disjoint(iPr_def_10,iPr_def_12)
| ( sK2 = sK3 ) ),
inference(superposition,[status(thm)],[c_165,c_317]) ).
tcf(c_425,plain,
disjoint(iPr_def_10,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_423,c_169]) ).
tcf(c_470,plain,
( disjoint(iPr_def_11,iPr_def_13)
| ~ disjoint(iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_166,c_338]) ).
tcf(c_478,plain,
disjoint(iPr_def_11,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_470,c_425]) ).
tcf(c_483,plain,
~ disjoint(iPr_def_14,iPr_def_15),
inference(backward_subsumption_resolution,[status(thm)],[c_170,c_478]) ).
tcf(c_773,plain,
( disjoint(iPr_def_14,iPr_def_15)
| ~ disjoint(iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_168,c_379]) ).
tcf(c_775,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_773,c_483,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET978+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n004.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Thu Sep 24 12:29:45 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 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
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.45 % Proving...
% 0.43/11.29 % SZS status Started for theBenchmark.p
% 0.43/11.29 % SZS status Theorem for theBenchmark.p
% 0.43/11.29
% 0.43/11.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.43/11.29
% 0.43/11.29 % ------ iProver source info
% 0.43/11.29
% 0.43/11.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.43/11.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.43/11.29 % git: non_committed_changes: false
% 0.43/11.29
% 0.43/11.29 % ------ Parsing...
% 0.43/11.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.43/11.29
% 0.43/11.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 0.43/11.29
% 0.43/11.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.43/11.29
% 0.43/11.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.43/11.29 % ------ Proving...
% 0.43/11.29 % ------ Problem Properties
% 0.43/11.29
% 0.43/11.29 %
% 0.43/11.29 % clauses 13
% 0.43/11.29 % conjectures 2
% 0.43/11.29 % EPR 4
% 0.43/11.29 % Horn 12
% 0.43/11.29 % unary 8
% 0.43/11.29 % binary 5
% 0.43/11.29 % lits 18
% 0.43/11.29 % lits eq 9
% 0.43/11.29 % fd_pure 0
% 0.43/11.29 % fd_pseudo 0
% 0.43/11.29 % fd_cond 0
% 0.43/11.29 % fd_pseudo_cond 1
% 0.43/11.29 % AC symbols 0
% 0.43/11.29
% 0.43/11.29 % ------ Schedule dynamic 5 is on
% 0.43/11.29
% 0.43/11.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.43/11.29
% 0.43/11.29
% 0.43/11.29 % ------
% 0.43/11.29 % Current options:
% 0.43/11.29 % ------
% 0.43/11.29
% 0.43/11.29
% 0.43/11.29 %
% 0.43/11.29
% 0.43/11.29 % ------ Proving...
% 0.43/11.29 %
% 0.43/11.29
% 0.43/11.29 % SZS status Theorem for theBenchmark.p
% 0.43/11.29
% 0.43/11.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/11.29
% 0.43/11.29
%------------------------------------------------------------------------------