TSTP Solution File: SEU239+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 : Thu Aug 31 17:05:06 EDT 2023
% Result : Theorem 2.14s 1.15s
% Output : CNFRefutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 11 unt; 0 def)
% Number of atoms : 223 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 265 ( 110 ~; 108 |; 30 &)
% ( 6 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn; 55 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f7,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(f9,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,plain,
? [X0] :
( ( reflexive(X0)
<~> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X0)
& in(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X0)
& in(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f58,f59]) ).
fof(f61,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f64,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f65,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(rectify,[],[f65]) ).
fof(f67,plain,
( ? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) )
=> ( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK2)
& in(X1,relation_field(sK2)) )
| ~ reflexive(sK2) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK2)
| ~ in(X2,relation_field(sK2)) )
| reflexive(sK2) )
& relation(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK2)
& in(X1,relation_field(sK2)) )
=> ( ~ in(ordered_pair(sK3,sK3),sK2)
& in(sK3,relation_field(sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
( ( ( ~ in(ordered_pair(sK3,sK3),sK2)
& in(sK3,relation_field(sK2)) )
| ~ reflexive(sK2) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK2)
| ~ in(X2,relation_field(sK2)) )
| reflexive(sK2) )
& relation(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f66,f68,f67]) ).
fof(f84,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f86,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f87,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK0(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f88,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f89,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f91,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f92,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f99,plain,
relation(sK2),
inference(cnf_transformation,[],[f69]) ).
fof(f100,plain,
! [X2] :
( in(ordered_pair(X2,X2),sK2)
| ~ in(X2,relation_field(sK2))
| reflexive(sK2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f101,plain,
( in(sK3,relation_field(sK2))
| ~ reflexive(sK2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f102,plain,
( ~ in(ordered_pair(sK3,sK3),sK2)
| ~ reflexive(sK2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f118,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK0(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f88,f89]) ).
fof(f119,plain,
! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f86,f89]) ).
fof(f121,plain,
( ~ in(unordered_pair(unordered_pair(sK3,sK3),singleton(sK3)),sK2)
| ~ reflexive(sK2) ),
inference(definition_unfolding,[],[f102,f89]) ).
fof(f122,plain,
! [X2] :
( in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),sK2)
| ~ in(X2,relation_field(sK2))
| reflexive(sK2) ),
inference(definition_unfolding,[],[f100,f89]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f84]) ).
cnf(c_53,plain,
( ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK0(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_54,plain,
( ~ relation(X0)
| in(sK0(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_55,plain,
( ~ in(X0,X1)
| ~ is_reflexive_in(X2,X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),X2) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_57,plain,
( ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0)
| reflexive(X0) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_58,plain,
( ~ relation(X0)
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_65,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK3,sK3),singleton(sK3)),sK2)
| ~ reflexive(sK2) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_66,negated_conjecture,
( ~ reflexive(sK2)
| in(sK3,relation_field(sK2)) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_67,negated_conjecture,
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(unordered_pair(X0,X0),singleton(X0)),sK2)
| reflexive(sK2) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_68,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f99]) ).
cnf(c_98,plain,
( ~ relation(sK2)
| ~ reflexive(sK2)
| is_reflexive_in(sK2,relation_field(sK2)) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_289,plain,
( ~ in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK3)),sK2)
| ~ reflexive(sK2) ),
inference(demodulation,[status(thm)],[c_65,c_51]) ).
cnf(c_298,plain,
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK2)
| reflexive(sK2) ),
inference(demodulation,[status(thm)],[c_67,c_51]) ).
cnf(c_305,plain,
( ~ in(X0,X1)
| ~ is_reflexive_in(X2,X1)
| ~ relation(X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X2) ),
inference(demodulation,[status(thm)],[c_55,c_51]) ).
cnf(c_314,plain,
( ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK0(X0,X1))),X0)
| ~ relation(X0)
| is_reflexive_in(X0,X1) ),
inference(demodulation,[status(thm)],[c_53,c_51]) ).
cnf(c_510,plain,
( X0 != sK2
| ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK0(X0,X1))),X0)
| is_reflexive_in(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_314,c_68]) ).
cnf(c_511,plain,
( ~ in(unordered_pair(singleton(sK0(sK2,X0)),unordered_pair(sK0(sK2,X0),sK0(sK2,X0))),sK2)
| is_reflexive_in(sK2,X0) ),
inference(unflattening,[status(thm)],[c_510]) ).
cnf(c_519,plain,
( X0 != sK2
| ~ reflexive(X0)
| is_reflexive_in(X0,relation_field(X0)) ),
inference(resolution_lifted,[status(thm)],[c_58,c_68]) ).
cnf(c_520,plain,
( ~ reflexive(sK2)
| is_reflexive_in(sK2,relation_field(sK2)) ),
inference(unflattening,[status(thm)],[c_519]) ).
cnf(c_527,plain,
( X0 != sK2
| ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0) ),
inference(resolution_lifted,[status(thm)],[c_57,c_68]) ).
cnf(c_528,plain,
( ~ is_reflexive_in(sK2,relation_field(sK2))
| reflexive(sK2) ),
inference(unflattening,[status(thm)],[c_527]) ).
cnf(c_540,plain,
( X0 != sK2
| in(sK0(X0,X1),X1)
| is_reflexive_in(X0,X1) ),
inference(resolution_lifted,[status(thm)],[c_54,c_68]) ).
cnf(c_541,plain,
( in(sK0(sK2,X0),X0)
| is_reflexive_in(sK2,X0) ),
inference(unflattening,[status(thm)],[c_540]) ).
cnf(c_666,plain,
( X0 != sK2
| ~ in(X1,X2)
| ~ is_reflexive_in(X0,X2)
| in(unordered_pair(singleton(X1),unordered_pair(X1,X1)),X0) ),
inference(resolution_lifted,[status(thm)],[c_305,c_68]) ).
cnf(c_667,plain,
( ~ in(X0,X1)
| ~ is_reflexive_in(sK2,X1)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK2) ),
inference(unflattening,[status(thm)],[c_666]) ).
cnf(c_773,plain,
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK2)
| is_reflexive_in(sK2,relation_field(sK2)) ),
inference(resolution,[status(thm)],[c_298,c_520]) ).
cnf(c_780,plain,
( ~ in(X0,relation_field(sK2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_773,c_667]) ).
cnf(c_3598,plain,
( ~ is_reflexive_in(sK2,relation_field(sK2))
| ~ reflexive(sK2)
| in(unordered_pair(singleton(sK3),unordered_pair(sK3,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_66,c_667]) ).
cnf(c_3603,plain,
~ reflexive(sK2),
inference(global_subsumption_just,[status(thm)],[c_3598,c_68,c_98,c_289,c_3598]) ).
cnf(c_3605,plain,
~ is_reflexive_in(sK2,relation_field(sK2)),
inference(backward_subsumption_resolution,[status(thm)],[c_528,c_3603]) ).
cnf(c_3628,plain,
( ~ in(sK0(sK2,X0),relation_field(sK2))
| is_reflexive_in(sK2,X0) ),
inference(superposition,[status(thm)],[c_780,c_511]) ).
cnf(c_3636,plain,
is_reflexive_in(sK2,relation_field(sK2)),
inference(superposition,[status(thm)],[c_541,c_3628]) ).
cnf(c_3637,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3636,c_3605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 19:57:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.14/1.15 % SZS status Started for theBenchmark.p
% 2.14/1.15 % SZS status Theorem for theBenchmark.p
% 2.14/1.15
% 2.14/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.14/1.15
% 2.14/1.15 ------ iProver source info
% 2.14/1.15
% 2.14/1.15 git: date: 2023-05-31 18:12:56 +0000
% 2.14/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.14/1.15 git: non_committed_changes: false
% 2.14/1.15 git: last_make_outside_of_git: false
% 2.14/1.15
% 2.14/1.15 ------ Parsing...
% 2.14/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.14/1.15
% 2.14/1.15 ------ Preprocessing... sup_sim: 5 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe_e
% 2.14/1.15
% 2.14/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.14/1.15
% 2.14/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.14/1.15 ------ Proving...
% 2.14/1.15 ------ Problem Properties
% 2.14/1.15
% 2.14/1.15
% 2.14/1.15 clauses 43
% 2.14/1.15 conjectures 1
% 2.14/1.15 EPR 8
% 2.14/1.15 Horn 38
% 2.14/1.15 unary 13
% 2.14/1.15 binary 25
% 2.14/1.15 lits 78
% 2.14/1.15 lits eq 10
% 2.14/1.15 fd_pure 0
% 2.14/1.15 fd_pseudo 0
% 2.14/1.15 fd_cond 1
% 2.14/1.15 fd_pseudo_cond 1
% 2.14/1.15 AC symbols 0
% 2.14/1.15
% 2.14/1.15 ------ Schedule dynamic 5 is on
% 2.14/1.15
% 2.14/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.14/1.15
% 2.14/1.15
% 2.14/1.15 ------
% 2.14/1.15 Current options:
% 2.14/1.15 ------
% 2.14/1.15
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% 2.14/1.15
% 2.14/1.15 ------ Proving...
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% 2.14/1.15 % SZS status Theorem for theBenchmark.p
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% 2.14/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 2.14/1.16
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