TSTP Solution File: SEU618^2 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU618^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 : Tue May 21 03:43:00 EDT 2024
% Result : Theorem 3.31s 1.86s
% Output : Refutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 8 unt; 8 typ; 2 def)
% Number of atoms : 41 ( 4 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 204 ( 16 ~; 7 |; 0 &; 171 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 31 ( 0 ^ 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(setunionI_type,type,
setunionI: $o ).
thf(setunionI_def,definition,
( setunionI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ C )
=> ( ( in @ C @ A )
=> ( in @ B @ ( setunion @ A ) ) ) ) ) ) ).
thf(secondinupair_type,type,
secondinupair: $o ).
thf(secondinupair_def,definition,
( secondinupair
= ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( setunionI
=> ( secondinupair
=> ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(2,negated_conjecture,
~ ( setunionI
=> ( secondinupair
=> ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ B @ C )
=> ( ( in @ C @ A )
=> ( in @ B @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ! [A: $i,B: $i] : ( in @ B @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ C )
| ~ ( in @ C @ A )
| ( in @ B @ ( setunion @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(4,plain,
~ ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ B @ C )
| ~ ( in @ C @ A )
| ( ( in @ B @ ( setunion @ A ) )
!= ( in @ sk2 @ ( setunion @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,4]) ).
thf(12,plain,
! [A: $i] :
( ~ ( in @ sk2 @ A )
| ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(pattern_uni,[status(thm)],[11:[bind(A,$thf( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(26,plain,
! [A: $i] :
( ~ ( in @ sk2 @ A )
| ~ ( in @ A @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ sk2 @ C )
| ( ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
!= ( in @ C @ ( setadjoin @ ( setadjoin @ sk1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,26]) ).
thf(34,plain,
~ ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( setadjoin @ sk1 @ emptyset )),bind(B,$thf( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )),bind(C,$thf( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ))]]) ).
thf(43,plain,
~ $true,
inference(rewrite,[status(thm)],[34,7]) ).
thf(44,plain,
$false,
inference(simp,[status(thm)],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU618^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 17:08:08 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.84/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.97 % [INFO] Parsing done (117ms).
% 1.11/0.98 % [INFO] Running in sequential loop mode.
% 1.65/1.22 % [INFO] nitpick registered as external prover.
% 1.66/1.23 % [INFO] Scanning for conjecture ...
% 1.84/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.32 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.33 % [INFO] Type checking passed.
% 1.84/1.33 % [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 ...
% 3.31/1.86 % [INFO] Killing All external provers ...
% 3.31/1.86 % Time passed: 1354ms (effective reasoning time: 875ms)
% 3.31/1.86 % 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)>
% 3.31/1.86 % Axioms used in derivation (0):
% 3.31/1.86 % No. of inferences in proof: 14
% 3.31/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1354 ms resp. 875 ms w/o parsing
% 3.31/1.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.31/1.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------