TSTP Solution File: SEU709_8 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU709_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 12:00:40 EDT 2023
% Result : Theorem 2.70s 1.62s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 23 ( 11 unt; 9 typ; 0 def)
% Number of atoms : 71 ( 18 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 151 ( 4 ~; 0 |; 1 &; 106 @)
% ( 1 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setadjoinIL_type,type,
setadjoinIL: $o ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(if_type,type,
if: $i > $o > $i > $i > $i ).
thf(iftrue_type,type,
iftrue: $o ).
thf(iffalse_type,type,
iffalse: $o ).
thf(7,axiom,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(25,plain,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
( secondinupair
= ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(21,plain,
( secondinupair
= ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
( iffalse
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ B
=> ( ( if @ A @ B @ C @ D )
= D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(17,plain,
( iffalse
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ~ B
=> ( ( if @ A @ B @ C @ D )
= D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
<=> ( in @ D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(23,plain,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( ( in @ C @ A )
=> ( in @ D @ B ) )
& ( ( in @ D @ B )
=> ( in @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1,conjecture,
( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(2,negated_conjecture,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( setadjoinIL
=> ( in__Cong
=> ( secondinupair
=> ( iftrue
=> ( iffalse
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( in @ ( if @ A @ B @ C @ D ) @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
( iftrue
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(19,plain,
( iftrue
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
$false,
inference(e,[status(thm)],[25,21,17,23,8,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU709_8 : TPTP v8.1.2. Released v8.0.0.
% 0.06/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 12:46:46 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (124ms).
% 1.20/0.96 % [INFO] Running in sequential loop mode.
% 1.61/1.16 % [INFO] eprover registered as external prover.
% 1.61/1.16 % [INFO] cvc4 registered as external prover.
% 1.61/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.20 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.71/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.71/1.21 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.71/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.71/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.89/1.25 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.99/1.27 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.99/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.28 % [INFO] Definitions in FOF are currently treated as axioms.
% 1.99/1.28 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.99/1.28 % [INFO] Type checking passed.
% 1.99/1.28 % [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 ...
% 2.70/1.61 % External prover 'e' found a proof!
% 2.70/1.61 % [INFO] Killing All external provers ...
% 2.70/1.62 % Time passed: 1104ms (effective reasoning time: 648ms)
% 2.70/1.62 % 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)>
% 2.70/1.62 % Axioms used in derivation (5): secondinupair, setadjoinIL, iffalse, in__Cong, iftrue
% 2.70/1.62 % No. of inferences in proof: 14
% 2.70/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1104 ms resp. 648 ms w/o parsing
% 3.10/1.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.10/1.71 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------