TSTP Solution File: SET949+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 15:10:47 EDT 2023
% Result : Theorem 1.87s 1.17s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 124 ( 51 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 149 ( 55 ~; 45 |; 43 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 121 ( 2 sgn; 82 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f8,conjecture,
! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t102_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(negated_conjecture,[],[f8]) ).
fof(f11,plain,
? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK0(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK0(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( sK0(X0,X1,X2) = ordered_pair(sK1(X0,X1,X2),sK2(X0,X1,X2))
& in(sK2(X0,X1,X2),X1)
& in(sK1(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
& in(sK4(X0,X1,X8),X1)
& in(sK3(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f13,f16,f15,f14]) ).
fof(f22,plain,
( ? [X0,X1,X2] :
( ! [X3,X4] : ordered_pair(X3,X4) != X0
& in(X0,cartesian_product2(X1,X2)) )
=> ( ! [X4,X3] : ordered_pair(X3,X4) != sK7
& in(sK7,cartesian_product2(sK8,sK9)) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ! [X3,X4] : ordered_pair(X3,X4) != sK7
& in(sK7,cartesian_product2(sK8,sK9)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f11,f22]) ).
fof(f25,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f28,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f38,plain,
in(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X3,X4] : ordered_pair(X3,X4) != sK7,
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f28,f34]) ).
fof(f45,plain,
! [X3,X4] : sK7 != unordered_pair(unordered_pair(X3,X4),singleton(X3)),
inference(definition_unfolding,[],[f39,f34]) ).
fof(f48,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK3(X0,X1,X8),sK4(X0,X1,X8)),singleton(sK3(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f43]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f25]) ).
cnf(c_56,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0)),singleton(sK3(X1,X2,X0))) = X0 ),
inference(cnf_transformation,[],[f48]) ).
cnf(c_62,negated_conjecture,
unordered_pair(unordered_pair(X0,X1),singleton(X0)) != sK7,
inference(cnf_transformation,[],[f45]) ).
cnf(c_63,negated_conjecture,
in(sK7,cartesian_product2(sK8,sK9)),
inference(cnf_transformation,[],[f38]) ).
cnf(c_139,plain,
unordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK7,
inference(demodulation,[status(thm)],[c_62,c_50]) ).
cnf(c_167,plain,
( ~ in(X0,cartesian_product2(X1,X2))
| unordered_pair(singleton(sK3(X1,X2,X0)),unordered_pair(sK3(X1,X2,X0),sK4(X1,X2,X0))) = X0 ),
inference(demodulation,[status(thm)],[c_56,c_50]) ).
cnf(c_574,plain,
unordered_pair(singleton(sK3(sK8,sK9,sK7)),unordered_pair(sK3(sK8,sK9,sK7),sK4(sK8,sK9,sK7))) = sK7,
inference(superposition,[status(thm)],[c_63,c_167]) ).
cnf(c_577,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_574,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n027.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 : Sat Aug 26 12:48:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.87/1.17 % SZS status Started for theBenchmark.p
% 1.87/1.17 % SZS status Theorem for theBenchmark.p
% 1.87/1.17
% 1.87/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.87/1.17
% 1.87/1.17 ------ iProver source info
% 1.87/1.17
% 1.87/1.17 git: date: 2023-05-31 18:12:56 +0000
% 1.87/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.87/1.17 git: non_committed_changes: false
% 1.87/1.17 git: last_make_outside_of_git: false
% 1.87/1.17
% 1.87/1.17 ------ Parsing...
% 1.87/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.87/1.17
% 1.87/1.17 ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe_e
% 1.87/1.17
% 1.87/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.87/1.17
% 1.87/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.87/1.17 ------ Proving...
% 1.87/1.17 ------ Problem Properties
% 1.87/1.17
% 1.87/1.17
% 1.87/1.17 clauses 15
% 1.87/1.17 conjectures 1
% 1.87/1.17 EPR 3
% 1.87/1.17 Horn 12
% 1.87/1.17 unary 6
% 1.87/1.17 binary 4
% 1.87/1.17 lits 31
% 1.87/1.17 lits eq 9
% 1.87/1.18 fd_pure 0
% 1.87/1.18 fd_pseudo 0
% 1.87/1.18 fd_cond 0
% 1.87/1.18 fd_pseudo_cond 4
% 1.87/1.18 AC symbols 0
% 1.87/1.18
% 1.87/1.18 ------ Schedule dynamic 5 is on
% 1.87/1.18
% 1.87/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.87/1.18
% 1.87/1.18
% 1.87/1.18 ------
% 1.87/1.18 Current options:
% 1.87/1.18 ------
% 1.87/1.18
% 1.87/1.18
% 1.87/1.18
% 1.87/1.18
% 1.87/1.18 ------ Proving...
% 1.87/1.18
% 1.87/1.18
% 1.87/1.18 % SZS status Theorem for theBenchmark.p
% 1.87/1.18
% 1.87/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.87/1.18
% 1.87/1.18
%------------------------------------------------------------------------------