TSTP Solution File: SEU177+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 03:04:51 EDT 2024
% Result : Theorem 4.07s 1.10s
% Output : CNFRefutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 17 unt; 0 def)
% Number of atoms : 205 ( 30 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 239 ( 93 ~; 91 |; 34 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 163 ( 6 sgn 98 !; 35 ?)
% 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] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f23,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(f94,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f95,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f94]) ).
fof(f131,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f160,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f161,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f202,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f95]) ).
fof(f203,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f202]) ).
fof(f290,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f160]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f290]) ).
fof(f292,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK15(X0,X1),X3),X0)
| ~ in(sK15(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK15(X0,X1),X4),X0)
| in(sK15(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK15(X0,X1),X4),X0)
=> in(ordered_pair(sK15(X0,X1),sK16(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK17(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK15(X0,X1),X3),X0)
| ~ in(sK15(X0,X1),X1) )
& ( in(ordered_pair(sK15(X0,X1),sK16(X0,X1)),X0)
| in(sK15(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK17(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f291,f294,f293,f292]) ).
fof(f307,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f308,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f307]) ).
fof(f309,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK22(X0,X1)),X0)
| ~ in(sK22(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK22(X0,X1)),X0)
| in(sK22(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f310,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK22(X0,X1)),X0)
=> in(ordered_pair(sK23(X0,X1),sK22(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK24(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK22(X0,X1)),X0)
| ~ in(sK22(X0,X1),X1) )
& ( in(ordered_pair(sK23(X0,X1),sK22(X0,X1)),X0)
| in(sK22(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK24(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f308,f311,f310,f309]) ).
fof(f344,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) )
=> ( ( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) )
& in(ordered_pair(sK34,sK35),sK36)
& relation(sK36) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
( ( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) )
& in(ordered_pair(sK34,sK35),sK36)
& relation(sK36) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36])],[f203,f344]) ).
fof(f369,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f427,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f444,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f312]) ).
fof(f448,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f525,plain,
relation(sK36),
inference(cnf_transformation,[],[f345]) ).
fof(f526,plain,
in(ordered_pair(sK34,sK35),sK36),
inference(cnf_transformation,[],[f345]) ).
fof(f527,plain,
( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) ),
inference(cnf_transformation,[],[f345]) ).
fof(f577,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f131]) ).
fof(f594,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f448,f577]) ).
fof(f612,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f427,f594]) ).
fof(f616,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f444,f594]) ).
fof(f642,plain,
in(unordered_pair(unordered_pair(sK34,sK35),unordered_pair(sK34,sK34)),sK36),
inference(definition_unfolding,[],[f526,f594]) ).
fof(f692,plain,
! [X0,X6,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f612]) ).
fof(f700,plain,
! [X0,X6,X5] :
( in(X5,relation_rng(X0))
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| ~ relation(X0) ),
inference(equality_resolution,[],[f616]) ).
cnf(c_51,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f369]) ).
cnf(c_110,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X0,relation_dom(X2)) ),
inference(cnf_transformation,[],[f692]) ).
cnf(c_127,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2)
| in(X1,relation_rng(X2)) ),
inference(cnf_transformation,[],[f700]) ).
cnf(c_206,negated_conjecture,
( ~ in(sK35,relation_rng(sK36))
| ~ in(sK34,relation_dom(sK36)) ),
inference(cnf_transformation,[],[f527]) ).
cnf(c_207,negated_conjecture,
in(unordered_pair(unordered_pair(sK34,sK35),unordered_pair(sK34,sK34)),sK36),
inference(cnf_transformation,[],[f642]) ).
cnf(c_208,negated_conjecture,
relation(sK36),
inference(cnf_transformation,[],[f525]) ).
cnf(c_2034,plain,
in(unordered_pair(unordered_pair(sK35,sK34),unordered_pair(sK34,sK34)),sK36),
inference(demodulation,[status(thm)],[c_207,c_51]) ).
cnf(c_2965,plain,
( X0 != sK36
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X0)
| in(X2,relation_rng(X0)) ),
inference(resolution_lifted,[status(thm)],[c_127,c_208]) ).
cnf(c_2966,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36)
| in(X1,relation_rng(sK36)) ),
inference(unflattening,[status(thm)],[c_2965]) ).
cnf(c_2974,plain,
( X0 != sK36
| ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X0)
| in(X1,relation_dom(X0)) ),
inference(resolution_lifted,[status(thm)],[c_110,c_208]) ).
cnf(c_2975,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36)
| in(X0,relation_dom(sK36)) ),
inference(unflattening,[status(thm)],[c_2974]) ).
cnf(c_3311,plain,
( in(X1,relation_rng(sK36))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36) ),
inference(prop_impl_just,[status(thm)],[c_2966]) ).
cnf(c_3312,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36)
| in(X1,relation_rng(sK36)) ),
inference(renaming,[status(thm)],[c_3311]) ).
cnf(c_3319,plain,
( in(X0,relation_dom(sK36))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36) ),
inference(prop_impl_just,[status(thm)],[c_2975]) ).
cnf(c_3320,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK36)
| in(X0,relation_dom(sK36)) ),
inference(renaming,[status(thm)],[c_3319]) ).
cnf(c_9292,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK36)
| in(X1,relation_dom(sK36)) ),
inference(superposition,[status(thm)],[c_51,c_3320]) ).
cnf(c_9300,plain,
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK36)
| in(X0,relation_rng(sK36)) ),
inference(superposition,[status(thm)],[c_51,c_3312]) ).
cnf(c_9396,plain,
in(sK34,relation_dom(sK36)),
inference(superposition,[status(thm)],[c_2034,c_9292]) ).
cnf(c_9414,plain,
in(sK35,relation_rng(sK36)),
inference(superposition,[status(thm)],[c_2034,c_9300]) ).
cnf(c_9419,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9414,c_9396,c_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.10 % Command : run_iprover %s %d THM
% 0.09/0.31 % Computer : n026.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Thu May 2 18:15:51 EDT 2024
% 0.09/0.31 % CPUTime :
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 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
% 4.07/1.10 % SZS status Started for theBenchmark.p
% 4.07/1.10 % SZS status Theorem for theBenchmark.p
% 4.07/1.10
% 4.07/1.10 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.07/1.10
% 4.07/1.10 ------ iProver source info
% 4.07/1.10
% 4.07/1.10 git: date: 2024-05-02 19:28:25 +0000
% 4.07/1.10 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.07/1.10 git: non_committed_changes: false
% 4.07/1.10
% 4.07/1.10 ------ Parsing...
% 4.07/1.10 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.07/1.10
% 4.07/1.10 ------ Preprocessing... sup_sim: 13 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
% 4.07/1.10
% 4.07/1.10 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.07/1.10
% 4.07/1.10 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.07/1.10 ------ Proving...
% 4.07/1.10 ------ Problem Properties
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 clauses 201
% 4.07/1.10 conjectures 1
% 4.07/1.10 EPR 28
% 4.07/1.10 Horn 154
% 4.07/1.10 unary 36
% 4.07/1.10 binary 84
% 4.07/1.10 lits 470
% 4.07/1.10 lits eq 116
% 4.07/1.10 fd_pure 0
% 4.07/1.10 fd_pseudo 0
% 4.07/1.10 fd_cond 18
% 4.07/1.10 fd_pseudo_cond 41
% 4.07/1.10 AC symbols 0
% 4.07/1.10
% 4.07/1.10 ------ Input Options Time Limit: Unbounded
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 ------
% 4.07/1.10 Current options:
% 4.07/1.10 ------
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 ------ Proving...
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 ------ Proving...
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 ------ Proving...
% 4.07/1.10
% 4.07/1.10
% 4.07/1.10 % SZS status Theorem for theBenchmark.p
% 4.07/1.10
% 4.07/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.07/1.10
% 4.07/1.11
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