TSTP Solution File: SET909+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 15:10:35 EDT 2023
% Result : Theorem 2.07s 1.16s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 41 ( 16 unt; 0 def)
% Number of atoms : 194 ( 84 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 244 ( 91 ~; 93 |; 51 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 111 ( 4 sgn; 84 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f5,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f13,conjecture,
! [X0,X1,X2] : empty_set != set_union2(unordered_pair(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] : empty_set != set_union2(unordered_pair(X0,X1),X2),
inference(negated_conjecture,[],[f13]) ).
fof(f19,plain,
? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X0,X1),X2),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK0(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| in(sK0(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f21,f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) )
=> ( ( ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ( ( ( sK1(X0,X1,X2) != X1
& sK1(X0,X1,X2) != X0 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X1
| sK1(X0,X1,X2) = X0
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X1 != X4
& X0 != X4 ) )
& ( X1 = X4
| X0 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f26,f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK2(X0,X1,X2),X1)
& ~ in(sK2(X0,X1,X2),X0) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( in(sK2(X0,X1,X2),X1)
| in(sK2(X0,X1,X2),X0)
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f31,f32]) ).
fof(f38,plain,
( ? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X0,X1),X2)
=> empty_set = set_union2(unordered_pair(sK5,sK6),sK7) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
empty_set = set_union2(unordered_pair(sK5,sK6),sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f19,f38]) ).
fof(f42,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f43,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f33]) ).
fof(f63,plain,
empty_set = set_union2(unordered_pair(sK5,sK6),sK7),
inference(cnf_transformation,[],[f39]) ).
fof(f64,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f43]) ).
fof(f65,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f47]) ).
fof(f66,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f65]) ).
fof(f70,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f53]) ).
cnf(c_51,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f42]) ).
cnf(c_53,plain,
~ in(X0,empty_set),
inference(cnf_transformation,[],[f64]) ).
cnf(c_57,plain,
in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f66]) ).
cnf(c_63,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f70]) ).
cnf(c_72,negated_conjecture,
set_union2(unordered_pair(sK5,sK6),sK7) = empty_set,
inference(cnf_transformation,[],[f63]) ).
cnf(c_189,plain,
set_union2(sK7,unordered_pair(sK5,sK6)) = empty_set,
inference(demodulation,[status(thm)],[c_72,c_51]) ).
cnf(c_578,plain,
( ~ in(X0,unordered_pair(sK5,sK6))
| in(X0,empty_set) ),
inference(superposition,[status(thm)],[c_189,c_63]) ).
cnf(c_582,plain,
~ in(X0,unordered_pair(sK5,sK6)),
inference(forward_subsumption_resolution,[status(thm)],[c_578,c_53]) ).
cnf(c_589,plain,
$false,
inference(superposition,[status(thm)],[c_57,c_582]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET909+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n020.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 13:04:45 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.07/1.16 % SZS status Started for theBenchmark.p
% 2.07/1.16 % SZS status Theorem for theBenchmark.p
% 2.07/1.16
% 2.07/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.07/1.16
% 2.07/1.16 ------ iProver source info
% 2.07/1.16
% 2.07/1.16 git: date: 2023-05-31 18:12:56 +0000
% 2.07/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.07/1.16 git: non_committed_changes: false
% 2.07/1.16 git: last_make_outside_of_git: false
% 2.07/1.16
% 2.07/1.16 ------ Parsing...
% 2.07/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.07/1.16
% 2.07/1.16 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.07/1.16
% 2.07/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.07/1.16
% 2.07/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.07/1.16 ------ Proving...
% 2.07/1.16 ------ Problem Properties
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16 clauses 24
% 2.07/1.16 conjectures 0
% 2.07/1.16 EPR 5
% 2.07/1.16 Horn 19
% 2.07/1.16 unary 10
% 2.07/1.16 binary 6
% 2.07/1.16 lits 48
% 2.07/1.16 lits eq 17
% 2.07/1.16 fd_pure 0
% 2.07/1.16 fd_pseudo 0
% 2.07/1.16 fd_cond 1
% 2.07/1.16 fd_pseudo_cond 6
% 2.07/1.16 AC symbols 0
% 2.07/1.16
% 2.07/1.16 ------ Schedule dynamic 5 is on
% 2.07/1.16
% 2.07/1.16 ------ no conjectures: strip conj schedule
% 2.07/1.16
% 2.07/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16 ------
% 2.07/1.16 Current options:
% 2.07/1.16 ------
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16 ------ Proving...
% 2.07/1.16
% 2.07/1.16
% 2.07/1.16 % SZS status Theorem for theBenchmark.p
% 2.07/1.16
% 2.07/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.07/1.16
% 2.07/1.16
%------------------------------------------------------------------------------