TSTP Solution File: SEU132+2 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 03:04:36 EDT 2024
% Result : Theorem 24.74s 4.20s
% Output : CNFRefutation 24.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 5 unt; 0 def)
% Number of atoms : 172 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 212 ( 84 ~; 81 |; 37 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 104 ( 2 sgn 74 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f35,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
inference(negated_conjecture,[],[f35]) ).
fof(f53,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f65,plain,
? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f85,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK2(X0,X1),X1)
& in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f86,f87]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( set_difference(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_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f95]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0)
| ~ in(sK4(X0,X1,X2),X2) )
& ( ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK4(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f96,f97]) ).
fof(f108,plain,
( ? [X0,X1,X2] :
( ~ subset(set_difference(X0,X2),set_difference(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10))
& subset(sK8,sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10))
& subset(sK8,sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f65,f108]) ).
fof(f128,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f129,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f130,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f137,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f98]) ).
fof(f167,plain,
subset(sK8,sK9),
inference(cnf_transformation,[],[f109]) ).
fof(f168,plain,
~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)),
inference(cnf_transformation,[],[f109]) ).
fof(f191,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f139]) ).
fof(f192,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f138]) ).
fof(f193,plain,
! [X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f137]) ).
cnf(c_63,plain,
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
cnf(c_64,plain,
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
cnf(c_65,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_75,plain,
( ~ in(X0,X1)
| in(X0,set_difference(X1,X2))
| in(X0,X2) ),
inference(cnf_transformation,[],[f191]) ).
cnf(c_76,plain,
( ~ in(X0,set_difference(X1,X2))
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f192]) ).
cnf(c_77,plain,
( ~ in(X0,set_difference(X1,X2))
| in(X0,X1) ),
inference(cnf_transformation,[],[f193]) ).
cnf(c_102,negated_conjecture,
~ subset(set_difference(sK8,sK10),set_difference(sK9,sK10)),
inference(cnf_transformation,[],[f168]) ).
cnf(c_103,negated_conjecture,
subset(sK8,sK9),
inference(cnf_transformation,[],[f167]) ).
cnf(c_1058,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
| subset(set_difference(sK8,sK10),set_difference(sK9,sK10)) ),
inference(instantiation,[status(thm)],[c_63]) ).
cnf(c_1059,plain,
( in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10))
| subset(set_difference(sK8,sK10),set_difference(sK9,sK10)) ),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_1075,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10))
| ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_1088,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9)
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK9,sK10))
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_75]) ).
cnf(c_1247,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),X0)
| ~ subset(X0,sK9)
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_6134,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),set_difference(sK8,sK10))
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8) ),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_33781,plain,
( ~ in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK8)
| ~ subset(sK8,sK9)
| in(sK2(set_difference(sK8,sK10),set_difference(sK9,sK10)),sK9) ),
inference(instantiation,[status(thm)],[c_1247]) ).
cnf(c_33786,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33781,c_6134,c_1088,c_1075,c_1058,c_1059,c_102,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n014.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 : Thu May 2 17:21:17 EDT 2024
% 0.14/0.34 % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.74/4.20 % SZS status Started for theBenchmark.p
% 24.74/4.20 % SZS status Theorem for theBenchmark.p
% 24.74/4.20
% 24.74/4.20 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 24.74/4.20
% 24.74/4.20 ------ iProver source info
% 24.74/4.20
% 24.74/4.20 git: date: 2024-05-02 19:28:25 +0000
% 24.74/4.20 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 24.74/4.20 git: non_committed_changes: false
% 24.74/4.20
% 24.74/4.20 ------ Parsing...
% 24.74/4.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 24.74/4.20
% 24.74/4.20 ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe_e sf_s rm: 1 0s sf_e pe_s pe_e
% 24.74/4.20
% 24.74/4.20 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e
% 24.74/4.20
% 24.74/4.20 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 24.74/4.20 ------ Proving...
% 24.74/4.20 ------ Problem Properties
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20 clauses 66
% 24.74/4.20 conjectures 2
% 24.74/4.20 EPR 17
% 24.74/4.20 Horn 52
% 24.74/4.20 unary 18
% 24.74/4.20 binary 27
% 24.74/4.20 lits 138
% 24.74/4.20 lits eq 30
% 24.74/4.20 fd_pure 0
% 24.74/4.20 fd_pseudo 0
% 24.74/4.20 fd_cond 3
% 24.74/4.20 fd_pseudo_cond 13
% 24.74/4.20 AC symbols 0
% 24.74/4.20
% 24.74/4.20 ------ Input Options Time Limit: Unbounded
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20 ------
% 24.74/4.20 Current options:
% 24.74/4.20 ------
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20 ------ Proving...
% 24.74/4.20
% 24.74/4.20
% 24.74/4.20 % SZS status Theorem for theBenchmark.p
% 24.74/4.20
% 24.74/4.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 24.74/4.20
% 24.74/4.20
%------------------------------------------------------------------------------