TSTP Solution File: SET983+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 15:10:55 EDT 2023
% Result : Theorem 1.66s 1.18s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 116 ( 13 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 141 ( 52 ~; 46 |; 37 &)
% ( 2 <=>; 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 : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn; 48 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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(f7,axiom,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4))) ),
inference(negated_conjecture,[],[f8]) ).
fof(f12,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f13,plain,
? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) ),
inference(flattening,[],[f12]) ).
fof(f14,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,[],[f3]) ).
fof(f15,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,[],[f14]) ).
fof(f16,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,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) )
| in(sK0(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ( ( ~ in(sK0(X0,X1,X2),X1)
| ~ in(sK0(X0,X1,X2),X0)
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK0(X0,X1,X2),X1)
& in(sK0(X0,X1,X2),X0) )
| in(sK0(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,[sK0])],[f16,f17]) ).
fof(f23,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X3),set_intersection2(X2,X4)))
& in(X0,cartesian_product2(X3,X4))
& in(X0,cartesian_product2(X1,X2)) )
=> ( ~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7)))
& in(sK3,cartesian_product2(sK6,sK7))
& in(sK3,cartesian_product2(sK4,sK5)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7)))
& in(sK3,cartesian_product2(sK6,sK7))
& in(sK3,cartesian_product2(sK4,sK5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f13,f23]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ in(X4,X0)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[],[f7]) ).
fof(f37,plain,
in(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f24]) ).
fof(f38,plain,
in(sK3,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f24]) ).
fof(f39,plain,
~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))),
inference(cnf_transformation,[],[f24]) ).
fof(f40,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f29]) ).
cnf(c_54,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X2,X1)) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,plain,
set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X2,X3)) = cartesian_product2(set_intersection2(X0,X2),set_intersection2(X1,X3)),
inference(cnf_transformation,[],[f36]) ).
cnf(c_61,negated_conjecture,
~ in(sK3,cartesian_product2(set_intersection2(sK4,sK6),set_intersection2(sK5,sK7))),
inference(cnf_transformation,[],[f39]) ).
cnf(c_62,negated_conjecture,
in(sK3,cartesian_product2(sK6,sK7)),
inference(cnf_transformation,[],[f38]) ).
cnf(c_63,negated_conjecture,
in(sK3,cartesian_product2(sK4,sK5)),
inference(cnf_transformation,[],[f37]) ).
cnf(c_139,plain,
~ in(sK3,set_intersection2(cartesian_product2(sK4,sK5),cartesian_product2(sK6,sK7))),
inference(demodulation,[status(thm)],[c_61,c_60]) ).
cnf(c_467,plain,
( ~ in(sK3,cartesian_product2(sK4,sK5))
| ~ in(sK3,cartesian_product2(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_54,c_139]) ).
cnf(c_468,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_467,c_62,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:00:08 EDT 2023
% 0.13/0.35 % 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
% 1.66/1.18 % SZS status Started for theBenchmark.p
% 1.66/1.18 % SZS status Theorem for theBenchmark.p
% 1.66/1.18
% 1.66/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.66/1.18
% 1.66/1.18 ------ iProver source info
% 1.66/1.18
% 1.66/1.18 git: date: 2023-05-31 18:12:56 +0000
% 1.66/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.66/1.18 git: non_committed_changes: false
% 1.66/1.18 git: last_make_outside_of_git: false
% 1.66/1.18
% 1.66/1.18 ------ Parsing...
% 1.66/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.66/1.18
% 1.66/1.18 ------ 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
% 1.66/1.18
% 1.66/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.66/1.18
% 1.66/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.66/1.18 ------ Proving...
% 1.66/1.18 ------ Problem Properties
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18 clauses 14
% 1.66/1.18 conjectures 2
% 1.66/1.18 EPR 2
% 1.66/1.18 Horn 12
% 1.66/1.18 unary 7
% 1.66/1.18 binary 3
% 1.66/1.18 lits 26
% 1.66/1.18 lits eq 7
% 1.66/1.18 fd_pure 0
% 1.66/1.18 fd_pseudo 0
% 1.66/1.18 fd_cond 0
% 1.66/1.18 fd_pseudo_cond 3
% 1.66/1.18 AC symbols 0
% 1.66/1.18
% 1.66/1.18 ------ Schedule dynamic 5 is on
% 1.66/1.18
% 1.66/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18 ------
% 1.66/1.18 Current options:
% 1.66/1.18 ------
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18 ------ Proving...
% 1.66/1.18
% 1.66/1.18
% 1.66/1.18 % SZS status Theorem for theBenchmark.p
% 1.66/1.18
% 1.66/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/1.18
% 1.66/1.18
%------------------------------------------------------------------------------