TSTP Solution File: SET880+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 15:10:27 EDT 2023
% Result : Theorem 1.76s 1.13s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 77 ( 50 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 87 ( 34 ~; 30 |; 16 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn; 29 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l36_zfmisc_1) ).
fof(f7,conjecture,
! [X0,X1] :
( empty_set = set_difference(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( empty_set = set_difference(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[],[f7]) ).
fof(f10,plain,
? [X0,X1] :
( X0 != X1
& empty_set = set_difference(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,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,[],[f2]) ).
fof(f12,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,[],[f11]) ).
fof(f13,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(f14,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])],[f12,f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( empty_set = set_difference(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f20,plain,
( ? [X0,X1] :
( X0 != X1
& empty_set = set_difference(singleton(X0),singleton(X1)) )
=> ( sK3 != sK4
& empty_set = set_difference(singleton(sK3),singleton(sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( sK3 != sK4
& empty_set = set_difference(singleton(sK3),singleton(sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f10,f20]) ).
fof(f23,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X0,X1] :
( in(X0,X1)
| empty_set != set_difference(singleton(X0),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
empty_set = set_difference(singleton(sK3),singleton(sK4)),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
sK3 != sK4,
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f23]) ).
cnf(c_53,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_56,plain,
( set_difference(singleton(X0),X1) != empty_set
| in(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_59,negated_conjecture,
sK3 != sK4,
inference(cnf_transformation,[],[f33]) ).
cnf(c_60,negated_conjecture,
set_difference(singleton(sK3),singleton(sK4)) = empty_set,
inference(cnf_transformation,[],[f32]) ).
cnf(c_459,plain,
in(sK3,singleton(sK4)),
inference(superposition,[status(thm)],[c_60,c_56]) ).
cnf(c_483,plain,
sK3 = sK4,
inference(superposition,[status(thm)],[c_459,c_53]) ).
cnf(c_484,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_483,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET880+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 10:37:02 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
% 1.76/1.13 % SZS status Started for theBenchmark.p
% 1.76/1.13 % SZS status Theorem for theBenchmark.p
% 1.76/1.13
% 1.76/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.76/1.13
% 1.76/1.13 ------ iProver source info
% 1.76/1.13
% 1.76/1.13 git: date: 2023-05-31 18:12:56 +0000
% 1.76/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.76/1.13 git: non_committed_changes: false
% 1.76/1.13 git: last_make_outside_of_git: false
% 1.76/1.13
% 1.76/1.13 ------ Parsing...
% 1.76/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.76/1.13
% 1.76/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 1.76/1.13
% 1.76/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.76/1.13
% 1.76/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.13 ------ Proving...
% 1.76/1.13 ------ Problem Properties
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13 clauses 12
% 1.76/1.13 conjectures 2
% 1.76/1.13 EPR 5
% 1.76/1.13 Horn 11
% 1.76/1.13 unary 6
% 1.76/1.13 binary 4
% 1.76/1.13 lits 20
% 1.76/1.13 lits eq 9
% 1.76/1.13 fd_pure 0
% 1.76/1.13 fd_pseudo 0
% 1.76/1.13 fd_cond 0
% 1.76/1.13 fd_pseudo_cond 2
% 1.76/1.13 AC symbols 0
% 1.76/1.13
% 1.76/1.13 ------ Schedule dynamic 5 is on
% 1.76/1.13
% 1.76/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13 ------
% 1.76/1.13 Current options:
% 1.76/1.13 ------
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13 ------ Proving...
% 1.76/1.13
% 1.76/1.13
% 1.76/1.13 % SZS status Theorem for theBenchmark.p
% 1.76/1.13
% 1.76/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.13
% 1.76/1.13
%------------------------------------------------------------------------------