TSTP Solution File: SEU267+2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 17:05:20 EDT 2023
% Result : Theorem 9.62s 2.16s
% Output : CNFRefutation 9.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 16 unt; 0 def)
% Number of atoms : 146 ( 145 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 170 ( 76 ~; 59 |; 18 &)
% ( 6 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 172 ( 5 sgn; 126 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f26,axiom,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X1] :
( pair_first(X0) = X1
<=> ! [X2,X3] :
( ordered_pair(X2,X3) = X0
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f36,axiom,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X1] :
( pair_second(X0) = X1
<=> ! [X2,X3] :
( ordered_pair(X2,X3) = X0
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f60,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(f317,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f325,conjecture,
! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f326,negated_conjecture,
~ ! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
inference(negated_conjecture,[],[f325]) ).
fof(f344,plain,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f26]) ).
fof(f345,plain,
! [X0] :
( ? [X1,X2] : ordered_pair(X1,X2) = X0
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f36]) ).
fof(f384,plain,
! [X0] :
( ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f344]) ).
fof(f389,plain,
! [X0] :
( ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(ennf_transformation,[],[f345]) ).
fof(f667,plain,
? [X0,X1] :
( pair_second(ordered_pair(X0,X1)) != X1
| pair_first(ordered_pair(X0,X1)) != X0 ),
inference(ennf_transformation,[],[f326]) ).
fof(f738,plain,
! [X0] :
( ! [X3] :
( ( pair_first(X0) = X3
| ? [X4,X5] :
( X3 != X4
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f384]) ).
fof(f739,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ? [X2,X3] :
( X1 != X2
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f738]) ).
fof(f740,plain,
! [X0,X1] :
( ? [X2,X3] :
( X1 != X2
& ordered_pair(X2,X3) = X0 )
=> ( sK20(X0,X1) != X1
& ordered_pair(sK20(X0,X1),sK21(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f741,plain,
! [X0] :
( ! [X1] :
( ( pair_first(X0) = X1
| ( sK20(X0,X1) != X1
& ordered_pair(sK20(X0,X1),sK21(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0 )
| pair_first(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f739,f740]) ).
fof(f775,plain,
! [X0] :
( ! [X3] :
( ( pair_second(X0) = X3
| ? [X4,X5] :
( X3 != X5
& ordered_pair(X4,X5) = X0 ) )
& ( ! [X4,X5] :
( X3 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X3 ) )
| ! [X1,X2] : ordered_pair(X1,X2) != X0 ),
inference(nnf_transformation,[],[f389]) ).
fof(f776,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ? [X2,X3] :
( X1 != X3
& ordered_pair(X2,X3) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(rectify,[],[f775]) ).
fof(f777,plain,
! [X0,X1] :
( ? [X2,X3] :
( X1 != X3
& ordered_pair(X2,X3) = X0 )
=> ( sK34(X0,X1) != X1
& ordered_pair(sK33(X0,X1),sK34(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f778,plain,
! [X0] :
( ! [X1] :
( ( pair_second(X0) = X1
| ( sK34(X0,X1) != X1
& ordered_pair(sK33(X0,X1),sK34(X0,X1)) = X0 ) )
& ( ! [X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0 )
| pair_second(X0) != X1 ) )
| ! [X6,X7] : ordered_pair(X6,X7) != X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f776,f777]) ).
fof(f1050,plain,
( ? [X0,X1] :
( pair_second(ordered_pair(X0,X1)) != X1
| pair_first(ordered_pair(X0,X1)) != X0 )
=> ( sK133 != pair_second(ordered_pair(sK132,sK133))
| sK132 != pair_first(ordered_pair(sK132,sK133)) ) ),
introduced(choice_axiom,[]) ).
fof(f1051,plain,
( sK133 != pair_second(ordered_pair(sK132,sK133))
| sK132 != pair_first(ordered_pair(sK132,sK133)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132,sK133])],[f667,f1050]) ).
fof(f1078,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f1143,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X4
| ordered_pair(X4,X5) != X0
| pair_first(X0) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f741]) ).
fof(f1179,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X5
| ordered_pair(X4,X5) != X0
| pair_second(X0) != X1
| ordered_pair(X6,X7) != X0 ),
inference(cnf_transformation,[],[f778]) ).
fof(f1288,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f60]) ).
fof(f1721,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f317]) ).
fof(f1732,plain,
( sK133 != pair_second(ordered_pair(sK132,sK133))
| sK132 != pair_first(ordered_pair(sK132,sK133)) ),
inference(cnf_transformation,[],[f1051]) ).
fof(f1761,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1288,f1721]) ).
fof(f1791,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X4
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| pair_first(X0) != X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1143,f1761,f1761]) ).
fof(f1806,plain,
! [X0,X1,X6,X7,X4,X5] :
( X1 = X5
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != X0
| pair_second(X0) != X1
| unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) != X0 ),
inference(definition_unfolding,[],[f1179,f1761,f1761]) ).
fof(f1949,plain,
( sK133 != pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132)))
| sK132 != pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) ),
inference(definition_unfolding,[],[f1732,f1761,f1761]) ).
fof(f1991,plain,
! [X1,X6,X7,X4,X5] :
( X1 = X4
| pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) ),
inference(equality_resolution,[],[f1791]) ).
fof(f1992,plain,
! [X6,X7,X4,X5] :
( pair_first(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X4
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) ),
inference(equality_resolution,[],[f1991]) ).
fof(f2012,plain,
! [X1,X6,X7,X4,X5] :
( X1 = X5
| pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) != X1
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) ),
inference(equality_resolution,[],[f1806]) ).
fof(f2013,plain,
! [X6,X7,X4,X5] :
( pair_second(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))) = X5
| unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)) != unordered_pair(unordered_pair(X6,X7),unordered_pair(X6,X6)) ),
inference(equality_resolution,[],[f2012]) ).
cnf(c_61,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1078]) ).
cnf(c_128,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0 ),
inference(cnf_transformation,[],[f1992]) ).
cnf(c_163,plain,
( unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2))
| pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1 ),
inference(cnf_transformation,[],[f2013]) ).
cnf(c_711,negated_conjecture,
( pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK132
| pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK133 ),
inference(cnf_transformation,[],[f1949]) ).
cnf(c_1626,plain,
( pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK133
| pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK132 ),
inference(prop_impl_just,[status(thm)],[c_711]) ).
cnf(c_1627,plain,
( pair_first(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK132
| pair_second(unordered_pair(unordered_pair(sK132,sK133),unordered_pair(sK132,sK132))) != sK133 ),
inference(renaming,[status(thm)],[c_1626]) ).
cnf(c_9103,plain,
( pair_first(unordered_pair(unordered_pair(sK133,sK132),unordered_pair(sK132,sK132))) != sK132
| pair_second(unordered_pair(unordered_pair(sK133,sK132),unordered_pair(sK132,sK132))) != sK133 ),
inference(demodulation,[status(thm)],[c_1627,c_61]) ).
cnf(c_15396,plain,
( pair_first(unordered_pair(unordered_pair(sK133,sK132),unordered_pair(sK132,sK132))) != sK132
| pair_second(unordered_pair(unordered_pair(sK133,sK132),unordered_pair(sK132,sK132))) != sK133 ),
inference(prop_impl_just,[status(thm)],[c_9103]) ).
cnf(c_39094,plain,
pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(equality_resolution,[status(thm)],[c_163]) ).
cnf(c_39109,plain,
pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(equality_resolution,[status(thm)],[c_128]) ).
cnf(c_39295,plain,
pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X1,
inference(global_subsumption_just,[status(thm)],[c_163,c_39094]) ).
cnf(c_39299,plain,
pair_second(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1))) = X0,
inference(superposition,[status(thm)],[c_61,c_39295]) ).
cnf(c_39301,plain,
pair_first(unordered_pair(unordered_pair(sK133,sK132),unordered_pair(sK132,sK132))) != sK132,
inference(backward_subsumption_resolution,[status(thm)],[c_15396,c_39299]) ).
cnf(c_39325,plain,
pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0))) = X0,
inference(global_subsumption_just,[status(thm)],[c_128,c_39109]) ).
cnf(c_39329,plain,
pair_first(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1))) = X1,
inference(superposition,[status(thm)],[c_61,c_39325]) ).
cnf(c_40125,plain,
$false,
inference(superposition,[status(thm)],[c_39329,c_39301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU267+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n017.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 : Wed Aug 23 18:25:39 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 9.62/2.16 % SZS status Started for theBenchmark.p
% 9.62/2.16 % SZS status Theorem for theBenchmark.p
% 9.62/2.16
% 9.62/2.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 9.62/2.16
% 9.62/2.16 ------ iProver source info
% 9.62/2.16
% 9.62/2.16 git: date: 2023-05-31 18:12:56 +0000
% 9.62/2.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 9.62/2.16 git: non_committed_changes: false
% 9.62/2.16 git: last_make_outside_of_git: false
% 9.62/2.16
% 9.62/2.16 ------ Parsing...
% 9.62/2.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.62/2.16
% 9.62/2.16 ------ Preprocessing... sup_sim: 66 sf_s rm: 6 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 9.62/2.16
% 9.62/2.16 ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e
% 9.62/2.16
% 9.62/2.16 ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 9.62/2.16 ------ Proving...
% 9.62/2.16 ------ Problem Properties
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16 clauses 618
% 9.62/2.16 conjectures 0
% 9.62/2.16 EPR 99
% 9.62/2.16 Horn 483
% 9.62/2.16 unary 82
% 9.62/2.16 binary 168
% 9.62/2.16 lits 1838
% 9.62/2.16 lits eq 297
% 9.62/2.16 fd_pure 0
% 9.62/2.16 fd_pseudo 0
% 9.62/2.16 fd_cond 21
% 9.62/2.16 fd_pseudo_cond 103
% 9.62/2.16 AC symbols 0
% 9.62/2.16
% 9.62/2.16 ------ Input Options Time Limit: Unbounded
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16 ------
% 9.62/2.16 Current options:
% 9.62/2.16 ------
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16 ------ Proving...
% 9.62/2.16
% 9.62/2.16
% 9.62/2.16 % SZS status Theorem for theBenchmark.p
% 9.62/2.16
% 9.62/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.62/2.16
% 9.62/2.16
%------------------------------------------------------------------------------