TSTP Solution File: SET930+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Fri May 3 03:02:02 EDT 2024
% Result : Theorem 4.06s 1.23s
% Output : CNFRefutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 127 ( 70 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 160 ( 74 ~; 47 |; 35 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
<=> ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
<=> ( ~ in(X1,X2)
& ~ in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(f8,axiom,
! [X0,X1,X2] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t73_zfmisc_1) ).
fof(f9,conjecture,
! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t74_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f9]) ).
fof(f12,plain,
? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ( X0 != X1
& ~ in(X1,X2) )
| in(X0,X2) )
& ( ( ( X0 = X1
| in(X1,X2) )
& ~ in(X0,X2) )
| set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) )
& ( ( ~ in(X1,X2)
& ~ in(X0,X2) )
| unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ? [X0,X1,X2] :
( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
& set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
& empty_set != set_difference(unordered_pair(X0,X1),X2) )
=> ( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
& empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3)
& set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2)
& empty_set != set_difference(unordered_pair(sK2,sK3),sK4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f12,f23]) ).
fof(f26,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X2,X0,X1] :
( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
| ~ in(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
| in(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( empty_set = set_difference(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
empty_set != set_difference(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
unordered_pair(sK2,sK3) != set_difference(unordered_pair(sK2,sK3),sK4),
inference(cnf_transformation,[],[f24]) ).
cnf(c_50,plain,
unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f26]) ).
cnf(c_53,plain,
( ~ in(X0,X1)
| set_difference(unordered_pair(X2,X0),X1) = singleton(X2)
| in(X2,X1) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_58,plain,
( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
| in(X0,X2)
| in(X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| ~ in(X2,X1)
| set_difference(unordered_pair(X2,X0),X1) = empty_set ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_64,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != unordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
cnf(c_65,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK3),
inference(cnf_transformation,[],[f42]) ).
cnf(c_66,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != singleton(sK2),
inference(cnf_transformation,[],[f41]) ).
cnf(c_67,negated_conjecture,
set_difference(unordered_pair(sK2,sK3),sK4) != empty_set,
inference(cnf_transformation,[],[f40]) ).
cnf(c_369,plain,
set_difference(unordered_pair(sK3,sK2),sK4) != singleton(sK3),
inference(demodulation,[status(thm)],[c_65,c_50]) ).
cnf(c_371,plain,
set_difference(unordered_pair(sK3,sK2),sK4) != empty_set,
inference(demodulation,[status(thm)],[c_67,c_50]) ).
cnf(c_485,plain,
( set_difference(unordered_pair(sK2,sK3),sK4) = unordered_pair(sK2,sK3)
| in(sK2,sK4)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_58]) ).
cnf(c_554,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(X0,sK2),sK4) = singleton(X0)
| in(X0,sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_971,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(X0,sK3),sK4) = singleton(X0)
| in(X0,sK4) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_972,plain,
( ~ in(sK3,sK4)
| set_difference(unordered_pair(sK2,sK3),sK4) = singleton(sK2)
| in(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_971]) ).
cnf(c_977,plain,
( ~ in(X0,sK4)
| ~ in(sK3,sK4)
| set_difference(unordered_pair(sK3,X0),sK4) = empty_set ),
inference(instantiation,[status(thm)],[c_61]) ).
cnf(c_978,plain,
( ~ in(sK2,sK4)
| ~ in(sK3,sK4)
| set_difference(unordered_pair(sK3,sK2),sK4) = empty_set ),
inference(instantiation,[status(thm)],[c_977]) ).
cnf(c_2225,plain,
( ~ in(sK2,sK4)
| set_difference(unordered_pair(sK3,sK2),sK4) = singleton(sK3)
| in(sK3,sK4) ),
inference(instantiation,[status(thm)],[c_554]) ).
cnf(c_2226,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2225,c_978,c_972,c_485,c_371,c_369,c_64,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : run_iprover %s %d THM
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 2 20:53:45 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 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
% 4.06/1.23 % SZS status Started for theBenchmark.p
% 4.06/1.23 % SZS status Theorem for theBenchmark.p
% 4.06/1.23
% 4.06/1.23 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.06/1.23
% 4.06/1.23 ------ iProver source info
% 4.06/1.23
% 4.06/1.23 git: date: 2024-05-02 19:28:25 +0000
% 4.06/1.23 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.06/1.23 git: non_committed_changes: false
% 4.06/1.23
% 4.06/1.23 ------ Parsing...
% 4.06/1.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.06/1.23
% 4.06/1.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 4.06/1.23
% 4.06/1.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.06/1.23
% 4.06/1.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.06/1.23 ------ Proving...
% 4.06/1.23 ------ Problem Properties
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23 clauses 19
% 4.06/1.23 conjectures 4
% 4.06/1.23 EPR 4
% 4.06/1.23 Horn 15
% 4.06/1.23 unary 8
% 4.06/1.23 binary 7
% 4.06/1.23 lits 34
% 4.06/1.23 lits eq 16
% 4.06/1.23 fd_pure 0
% 4.06/1.23 fd_pseudo 0
% 4.06/1.23 fd_cond 0
% 4.06/1.23 fd_pseudo_cond 1
% 4.06/1.23 AC symbols 0
% 4.06/1.23
% 4.06/1.23 ------ Input Options Time Limit: Unbounded
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23 ------
% 4.06/1.23 Current options:
% 4.06/1.23 ------
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23 ------ Proving...
% 4.06/1.23
% 4.06/1.23
% 4.06/1.23 % SZS status Theorem for theBenchmark.p
% 4.06/1.23
% 4.06/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.06/1.23
% 4.06/1.24
%------------------------------------------------------------------------------