TSTP Solution File: SET918+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n019.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 15:10:38 EDT 2023
% Result : Theorem 2.46s 1.18s
% Output : CNFRefutation 2.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 245 ( 113 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 313 ( 115 ~; 116 |; 72 &)
% ( 6 <=>; 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; 3 con; 0-3 aty)
% Number of variables : 118 ( 1 sgn; 91 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f4,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f10,conjecture,
! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_zfmisc_1) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] :
~ ( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(negated_conjecture,[],[f10]) ).
fof(f14,plain,
? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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(f23,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])],[f21,f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f25]) ).
fof(f27,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(f28,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f26,f27]) ).
fof(f33,plain,
( ? [X0,X1,X2] :
( X0 != X1
& in(X1,X2)
& singleton(X0) = set_intersection2(unordered_pair(X0,X1),X2) )
=> ( sK5 != sK6
& in(sK6,sK7)
& singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( sK5 != sK6
& in(sK6,sK7)
& singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f14,f33]) ).
fof(f37,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f38,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f44,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f50,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f28]) ).
fof(f57,plain,
singleton(sK5) = set_intersection2(unordered_pair(sK5,sK6),sK7),
inference(cnf_transformation,[],[f34]) ).
fof(f58,plain,
in(sK6,sK7),
inference(cnf_transformation,[],[f34]) ).
fof(f59,plain,
sK5 != sK6,
inference(cnf_transformation,[],[f34]) ).
fof(f62,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f38]) ).
fof(f63,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f44]) ).
fof(f64,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f63]) ).
fof(f68,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f50]) ).
cnf(c_51,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f37]) ).
cnf(c_55,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f62]) ).
cnf(c_59,plain,
in(X0,unordered_pair(X1,X0)),
inference(cnf_transformation,[],[f64]) ).
cnf(c_65,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(cnf_transformation,[],[f68]) ).
cnf(c_71,negated_conjecture,
sK5 != sK6,
inference(cnf_transformation,[],[f59]) ).
cnf(c_72,negated_conjecture,
in(sK6,sK7),
inference(cnf_transformation,[],[f58]) ).
cnf(c_73,negated_conjecture,
set_intersection2(unordered_pair(sK5,sK6),sK7) = singleton(sK5),
inference(cnf_transformation,[],[f57]) ).
cnf(c_191,plain,
set_intersection2(sK7,unordered_pair(sK5,sK6)) = singleton(sK5),
inference(demodulation,[status(thm)],[c_73,c_51]) ).
cnf(c_825,plain,
( ~ in(X0,unordered_pair(sK5,sK6))
| ~ in(X0,sK7)
| in(X0,singleton(sK5)) ),
inference(superposition,[status(thm)],[c_191,c_65]) ).
cnf(c_915,plain,
( ~ in(sK6,sK7)
| in(sK6,singleton(sK5)) ),
inference(superposition,[status(thm)],[c_59,c_825]) ).
cnf(c_918,plain,
in(sK6,singleton(sK5)),
inference(forward_subsumption_resolution,[status(thm)],[c_915,c_72]) ).
cnf(c_925,plain,
sK5 = sK6,
inference(superposition,[status(thm)],[c_918,c_55]) ).
cnf(c_927,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_925,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.18/0.35 % Computer : n019.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Sat Aug 26 14:20:28 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.46/1.18 % SZS status Started for theBenchmark.p
% 2.46/1.18 % SZS status Theorem for theBenchmark.p
% 2.46/1.18
% 2.46/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.46/1.18
% 2.46/1.18 ------ iProver source info
% 2.46/1.18
% 2.46/1.18 git: date: 2023-05-31 18:12:56 +0000
% 2.46/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.46/1.18 git: non_committed_changes: false
% 2.46/1.18 git: last_make_outside_of_git: false
% 2.46/1.18
% 2.46/1.18 ------ Parsing...
% 2.46/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.46/1.18
% 2.46/1.18 ------ Preprocessing... sup_sim: 1 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
% 2.46/1.18
% 2.46/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.46/1.18
% 2.46/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.46/1.18 ------ Proving...
% 2.46/1.18 ------ Problem Properties
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18 clauses 24
% 2.46/1.18 conjectures 2
% 2.46/1.18 EPR 4
% 2.46/1.18 Horn 19
% 2.46/1.18 unary 10
% 2.46/1.18 binary 4
% 2.46/1.18 lits 50
% 2.46/1.18 lits eq 23
% 2.46/1.18 fd_pure 0
% 2.46/1.18 fd_pseudo 0
% 2.46/1.18 fd_cond 0
% 2.46/1.18 fd_pseudo_cond 8
% 2.46/1.18 AC symbols 0
% 2.46/1.18
% 2.46/1.18 ------ Schedule dynamic 5 is on
% 2.46/1.18
% 2.46/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18 ------
% 2.46/1.18 Current options:
% 2.46/1.18 ------
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18 ------ Proving...
% 2.46/1.18
% 2.46/1.18
% 2.46/1.18 % SZS status Theorem for theBenchmark.p
% 2.46/1.18
% 2.46/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.46/1.18
% 2.46/1.18
%------------------------------------------------------------------------------