TSTP Solution File: SEU165+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 03:04:48 EDT 2024
% Result : Theorem 3.82s 1.17s
% Output : CNFRefutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 13 unt; 0 def)
% Number of atoms : 132 ( 8 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 135 ( 55 ~; 57 |; 18 &)
% ( 3 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 106 ( 9 sgn 56 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f17,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(f46,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f51,conjecture,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f52,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
inference(negated_conjecture,[],[f51]) ).
fof(f85,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f118,plain,
? [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<~> ( in(X1,X3)
& in(X0,X2) ) ),
inference(ennf_transformation,[],[f52]) ).
fof(f202,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f203,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f202]) ).
fof(f208,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f209,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f208]) ).
fof(f210,plain,
( ? [X0,X1,X2,X3] :
( ( ~ in(X1,X3)
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) )
& ( ( in(X1,X3)
& in(X0,X2) )
| in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) )
=> ( ( ~ in(sK19,sK21)
| ~ in(sK18,sK20)
| ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) )
& ( ( in(sK19,sK21)
& in(sK18,sK20) )
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
( ( ~ in(sK19,sK21)
| ~ in(sK18,sK20)
| ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) )
& ( ( in(sK19,sK21)
& in(sK18,sK20) )
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f209,f210]) ).
fof(f229,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f286,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f310,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f311,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f312,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f203]) ).
fof(f317,plain,
( in(sK18,sK20)
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f318,plain,
( in(sK19,sK21)
| in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f319,plain,
( ~ in(sK19,sK21)
| ~ in(sK18,sK20)
| ~ in(ordered_pair(sK18,sK19),cartesian_product2(sK20,sK21)) ),
inference(cnf_transformation,[],[f211]) ).
fof(f364,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f85]) ).
fof(f377,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f286,f364]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f312,f377]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f311,f377]) ).
fof(f409,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f310,f377]) ).
fof(f410,plain,
( ~ in(sK19,sK21)
| ~ in(sK18,sK20)
| ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f319,f377]) ).
fof(f411,plain,
( in(sK19,sK21)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f318,f377]) ).
fof(f412,plain,
( in(sK18,sK20)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(definition_unfolding,[],[f317,f377]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f229]) ).
cnf(c_131,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X2,X2)),cartesian_product2(X3,X1)) ),
inference(cnf_transformation,[],[f407]) ).
cnf(c_132,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f408]) ).
cnf(c_133,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f409]) ).
cnf(c_138,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| ~ in(sK19,sK21)
| ~ in(sK18,sK20) ),
inference(cnf_transformation,[],[f410]) ).
cnf(c_139,negated_conjecture,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK19,sK21) ),
inference(cnf_transformation,[],[f411]) ).
cnf(c_140,negated_conjecture,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK18,sK20) ),
inference(cnf_transformation,[],[f412]) ).
cnf(c_338,plain,
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_133]) ).
cnf(c_339,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(renaming,[status(thm)],[c_338]) ).
cnf(c_342,plain,
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(prop_impl_just,[status(thm)],[c_132]) ).
cnf(c_343,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(renaming,[status(thm)],[c_342]) ).
cnf(c_390,plain,
( in(sK19,sK21)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(prop_impl_just,[status(thm)],[c_139]) ).
cnf(c_391,plain,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK19,sK21) ),
inference(renaming,[status(thm)],[c_390]) ).
cnf(c_392,plain,
( in(sK18,sK20)
| in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)) ),
inference(prop_impl_just,[status(thm)],[c_140]) ).
cnf(c_393,plain,
( in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| in(sK18,sK20) ),
inference(renaming,[status(thm)],[c_392]) ).
cnf(c_935,plain,
in(sK19,sK21),
inference(forward_subsumption_resolution,[status(thm)],[c_391,c_343]) ).
cnf(c_939,plain,
( ~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21))
| ~ in(sK18,sK20) ),
inference(backward_subsumption_resolution,[status(thm)],[c_138,c_935]) ).
cnf(c_942,plain,
in(sK18,sK20),
inference(forward_subsumption_resolution,[status(thm)],[c_393,c_339]) ).
cnf(c_946,plain,
~ in(unordered_pair(unordered_pair(sK18,sK19),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)),
inference(backward_subsumption_resolution,[status(thm)],[c_939,c_942]) ).
cnf(c_1429,plain,
~ in(unordered_pair(unordered_pair(sK19,sK18),unordered_pair(sK18,sK18)),cartesian_product2(sK20,sK21)),
inference(demodulation,[status(thm)],[c_946,c_51]) ).
cnf(c_5391,plain,
( ~ in(X0,X1)
| ~ in(X2,X3)
| in(unordered_pair(unordered_pair(X2,X0),unordered_pair(X0,X0)),cartesian_product2(X1,X3)) ),
inference(superposition,[status(thm)],[c_51,c_131]) ).
cnf(c_5503,plain,
( ~ in(sK19,sK21)
| ~ in(sK18,sK20) ),
inference(superposition,[status(thm)],[c_5391,c_1429]) ).
cnf(c_5508,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5503,c_942,c_935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 17:58:31 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.82/1.17 % SZS status Started for theBenchmark.p
% 3.82/1.17 % SZS status Theorem for theBenchmark.p
% 3.82/1.17
% 3.82/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.82/1.17
% 3.82/1.17 ------ iProver source info
% 3.82/1.17
% 3.82/1.17 git: date: 2024-05-02 19:28:25 +0000
% 3.82/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.82/1.17 git: non_committed_changes: false
% 3.82/1.17
% 3.82/1.17 ------ Parsing...
% 3.82/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.82/1.17
% 3.82/1.17 ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.82/1.17
% 3.82/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.82/1.17
% 3.82/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.82/1.17 ------ Proving...
% 3.82/1.17 ------ Problem Properties
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17 clauses 127
% 3.82/1.17 conjectures 0
% 3.82/1.17 EPR 23
% 3.82/1.17 Horn 98
% 3.82/1.17 unary 28
% 3.82/1.17 binary 55
% 3.82/1.17 lits 277
% 3.82/1.17 lits eq 81
% 3.82/1.17 fd_pure 0
% 3.82/1.17 fd_pseudo 0
% 3.82/1.17 fd_cond 3
% 3.82/1.17 fd_pseudo_cond 35
% 3.82/1.17 AC symbols 0
% 3.82/1.17
% 3.82/1.17 ------ Input Options Time Limit: Unbounded
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17 ------
% 3.82/1.17 Current options:
% 3.82/1.17 ------
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17 ------ Proving...
% 3.82/1.17
% 3.82/1.17
% 3.82/1.17 % SZS status Theorem for theBenchmark.p
% 3.82/1.17
% 3.82/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.82/1.17
% 3.82/1.18
%------------------------------------------------------------------------------