TSTP Solution File: SEU527_8 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU527_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 19 11:59:32 EDT 2023
% Result : Theorem 4.62s 2.17s
% Output : Refutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 69 ( 23 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 141 ( 10 ~; 18 |; 0 &; 80 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 51 ( 0 ^; 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(emptysetE_type,type,
emptysetE: $o ).
thf(setadjoinE_type,type,
setadjoinE: $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( emptysetE
=> ( setadjoinE
=> ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( setadjoinE
=> ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ( emptysetE
=> ( setadjoinE
=> ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
in @ sk1 @ ( setadjoin @ sk2 @ emptyset ),
inference(cnf,[status(esa)],[5]) ).
thf(3,axiom,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(11,plain,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,plain,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(8,plain,
setadjoinE,
inference(cnf,[status(esa)],[5]) ).
thf(41,plain,
! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ),
inference(rewrite,[status(thm)],[12,8]) ).
thf(44,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( C = A )
| ( in @ C @ B )
| D ),
inference(cnf,[status(esa)],[41]) ).
thf(72,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ~ ( in @ C @ ( setadjoin @ A @ B ) )
| ( in @ C @ B )
| D ),
inference(lifteq,[status(thm)],[44]) ).
thf(111,plain,
! [D: $o,C: $i,B: $i,A: $i] :
( ( C = A )
| ( in @ C @ B )
| D
| ( ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( in @ C @ ( setadjoin @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,72]) ).
thf(112,plain,
! [A: $o] :
( ( sk2 = sk1 )
| ( in @ sk1 @ emptyset )
| A ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( sk2 )),bind(B,$thf( emptyset )),bind(C,$thf( sk1 ))]]) ).
thf(154,plain,
! [A: $o] :
( ( sk2 = sk1 )
| ( in @ sk1 @ emptyset )
| A ),
inference(simp,[status(thm)],[112]) ).
thf(4,axiom,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(13,plain,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,plain,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(9,plain,
emptysetE,
inference(cnf,[status(esa)],[5]) ).
thf(15,plain,
! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ),
inference(rewrite,[status(thm)],[14,9]) ).
thf(16,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnf,[status(esa)],[15]) ).
thf(24,plain,
! [A: $i] :
( ~ ( in @ A @ emptyset )
| $false ),
inference(prim_subst,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( $false ))]]) ).
thf(33,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(simp,[status(thm)],[24]) ).
thf(227,plain,
! [A: $o] :
( ( sk2 = sk1 )
| $false
| A ),
inference(rewrite,[status(thm)],[154,33]) ).
thf(228,plain,
! [A: $o] :
( ( sk2 = sk1 )
| A ),
inference(simp,[status(thm)],[227]) ).
thf(6,plain,
sk1 != sk2,
inference(cnf,[status(esa)],[5]) ).
thf(10,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(229,plain,
! [A: $o] : A,
inference(simplifyReflect,[status(thm)],[228,10]) ).
thf(237,plain,
$false,
inference(prim_subst,[status(thm)],[229:[bind(A,$thf( $false ))]]) ).
thf(249,plain,
$false,
inference(simp,[status(thm)],[237]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU527_8 : TPTP v8.1.2. Released v8.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n026.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 13:45:51 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.00 % [INFO] Parsing done (131ms).
% 1.16/1.01 % [INFO] Running in sequential loop mode.
% 1.69/1.25 % [INFO] eprover registered as external prover.
% 1.69/1.26 % [INFO] cvc4 registered as external prover.
% 1.69/1.26 % [INFO] Scanning for conjecture ...
% 1.69/1.30 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.86/1.31 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.86/1.33 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.86/1.36 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.06/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.36 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.06/1.36 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.06/1.37 % [INFO] Type checking passed.
% 2.06/1.37 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.62/2.17 % [INFO] Killing All external provers ...
% 4.62/2.17 % Time passed: 1650ms (effective reasoning time: 1154ms)
% 4.62/2.17 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.62/2.17 % Axioms used in derivation (2): setadjoinE, emptysetE
% 4.62/2.17 % No. of inferences in proof: 29
% 4.62/2.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1650 ms resp. 1154 ms w/o parsing
% 4.62/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.62/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------