%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n001.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 02:56:24 PM UTC 2026
% Result : Theorem 2.37s 1.19s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 10 unt; 0 def)
% Number of atoms : 140 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 139 ( 61 ~; 54 |; 12 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 7 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn 138 !; 8 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( relation_of2(X2,X0,X1)
<=> subset(X2,cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relset_1) ).
fof(f9,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f13,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f16,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t14_relset_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
=> ( subset(relation_rng(X3),X1)
=> relation_of2_as_subset(X3,X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X2,X0,X1)
| ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f28,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
& subset(relation_rng(X3),X1)
& ~ relation_of2_as_subset(X3,X2,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f29,plain,
? [X0,X1,X2,X3] :
( relation_of2_as_subset(X3,X2,X0)
& subset(relation_rng(X3),X1)
& ~ relation_of2_as_subset(X3,X2,X1) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(ennf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ~ relation_of2(X2,X0,X1)
| subset(X2,cartesian_product2(X0,X1)) )
& ( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
& ( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f38,plain,
( relation_of2_as_subset(sK6,sK5,sK3)
& subset(relation_rng(sK6),sK4)
& ~ relation_of2_as_subset(sK6,sK5,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f29]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ subset(X2,cartesian_product2(X0,X1))
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(cnf_transformation,[],[f24]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| subset(relation_dom(X2),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f53,plain,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f38]) ).
fof(f54,plain,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f55,plain,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X3,X1))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_62,negated_conjecture,
~ relation_of2_as_subset(sK6,sK5,sK4),
inference(cnf_transformation,[],[f55]) ).
tcf(c_63,negated_conjecture,
subset(relation_rng(sK6),sK4),
inference(cnf_transformation,[],[f54]) ).
tcf(c_64,negated_conjecture,
relation_of2_as_subset(sK6,sK5,sK3),
inference(cnf_transformation,[],[f53]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_66,plain,
! [X0: $i] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_56,c_50]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation_of2_as_subset(X0,X1,X2)
| ~ subset(X0,cartesian_product2(X1,X2)) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_100]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_60]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] :
( relation(X0)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[c_101,c_98]) ).
tcf(c_337,plain,
~ subset(sK6,cartesian_product2(sK5,sK4)),
inference(resolution,[status(thm)],[c_89,c_62]) ).
tcf(c_341,plain,
relation(sK6),
inference(resolution,[status(thm)],[c_239,c_64]) ).
tcf(c_353,plain,
subset(relation_dom(sK6),sK5),
inference(resolution,[status(thm)],[c_104,c_64]) ).
tcf(c_443,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,cartesian_product2(relation_dom(X0_iProver_subset_1),relation_rng(X0_iProver_subset_1)))
| ~ relation(X0_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_444,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X2_iProver_subset_1)
| ~ subset(X1_iProver_subset_1,X2_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_446,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1,X3_iProver_subset_1: iProver_subset_1] :
( subset(cartesian_product2(X2_iProver_subset_1,X0_iProver_subset_1),cartesian_product2(X3_iProver_subset_1,X1_iProver_subset_1))
| ~ subset(X2_iProver_subset_1,X3_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_59]) ).
tcf(c_635,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ relation(X0_iProver_subset_1)
| ~ subset(cartesian_product2(relation_dom(X0_iProver_subset_1),relation_rng(X0_iProver_subset_1)),X1_iProver_subset_1) ),
inference(superposition,[status(thm)],[c_443,c_444]) ).
tcf(c_2591,plain,
( subset(sK6,cartesian_product2(sK5,sK4))
| ~ relation(sK6)
| ~ subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4)) ),
inference(instantiation,[status(thm)],[c_635]) ).
tcf(c_2741,plain,
( subset(cartesian_product2(relation_dom(sK6),relation_rng(sK6)),cartesian_product2(sK5,sK4))
| ~ subset(relation_rng(sK6),sK4)
| ~ subset(relation_dom(sK6),sK5) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_2742,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2741,c_2591,c_353,c_341,c_337,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.37 % Computer : n001.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 13:32:53 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 2.37/1.19 % SZS status Started for theBenchmark.p
% 2.37/1.19 % SZS status Theorem for theBenchmark.p
% 2.37/1.19
% 2.37/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.37/1.19
% 2.37/1.19 % ------ iProver source info
% 2.37/1.19
% 2.37/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 2.37/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.37/1.19 % git: non_committed_changes: false
% 2.37/1.19
% 2.37/1.19 % ------ Parsing...
% 2.37/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.37/1.19
% 2.37/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e %
% 2.37/1.19
% 2.37/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.37/1.19 % ------ Proving...
% 2.37/1.19 % ------ Problem Properties
% 2.37/1.19
% 2.37/1.19 %
% 2.37/1.19 % clauses 23
% 2.37/1.19 % conjectures 1
% 2.37/1.19 % EPR 3
% 2.37/1.19 % Horn 23
% 2.37/1.19 % unary 17
% 2.37/1.19 % binary 4
% 2.37/1.19 % lits 31
% 2.37/1.19 % lits eq 0
% 2.37/1.19 % fd_pure 0
% 2.37/1.19 % fd_pseudo 0
% 2.37/1.19 % fd_cond 0
% 2.37/1.19 % fd_pseudo_cond 0
% 2.37/1.19 % AC symbols 0
% 2.37/1.19
% 2.37/1.19 % ------ Input Options Time Limit: Unbounded
% 2.37/1.19
% 2.37/1.19
% 2.37/1.19 % ------
% 2.37/1.19 % Current options:
% 2.37/1.19 % ------
% 2.37/1.19
% 2.37/1.19
% 2.37/1.19 %
% 2.37/1.19
% 2.37/1.19 % ------ Proving...
% 2.37/1.19 %
% 2.37/1.19
% 2.37/1.19 % SZS status Theorem for theBenchmark.p
% 2.37/1.19
% 2.37/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.37/1.19
% 2.37/1.19
%------------------------------------------------------------------------------