TSTP Solution File: SEU652^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% 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 : Tue May 21 03:43:10 EDT 2024
% Result : Theorem 6.45s 3.06s
% Output : Refutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 18 unt; 9 typ; 3 def)
% Number of atoms : 75 ( 39 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 242 ( 33 ~; 14 |; 0 &; 176 @)
% ( 0 <=>; 19 =>; 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 : 11 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 0 ^ 56 !; 1 ?; 57 :)
% 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(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
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(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [A: $i,B: $i,C: $i] :
( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(2,negated_conjecture,
~ ( setadjoinIL
=> ( uniqinunit
=> ( secondinupair
=> ! [A: $i,B: $i,C: $i] :
( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
=> ! [A: $i,B: $i] :
( ? [C: $i] :
( ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) )
= ( setadjoin @ C @ emptyset ) )
=> ( A = B ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(9,plain,
! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
! [B: $i,A: $i] : ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( in @ A @ ( setadjoin @ B @ emptyset ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(7,plain,
( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
= ( setadjoin @ sk3 @ emptyset ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
( ( setadjoin @ sk3 @ emptyset )
= ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(6,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
sk1 != sk2,
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[8]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk1 )
| ( B != sk2 ) ),
inference(paramod_ordered,[status(thm)],[11,14]) ).
thf(46,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk2 @ emptyset ) )
| ( A != sk1 ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(153,plain,
~ ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ),
inference(simp,[status(thm)],[46]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ B ) )
!= ( in @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[6,153]) ).
thf(241,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( ( setadjoin @ A @ B )
!= ( setadjoin @ sk2 @ emptyset ) ) ),
inference(simp,[status(thm)],[219]) ).
thf(249,plain,
! [A: $i] :
( ( setadjoin @ sk1 @ A )
!= ( setadjoin @ sk2 @ emptyset ) ),
inference(simp,[status(thm)],[241]) ).
thf(275,plain,
! [A: $i] :
( ( ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) )
!= ( setadjoin @ sk1 @ A ) )
| ( ( setadjoin @ sk3 @ emptyset )
!= ( setadjoin @ sk2 @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[13,249]) ).
thf(298,plain,
! [A: $i] :
( ( sk1 != sk1 )
| ( ( setadjoin @ sk2 @ emptyset )
!= A )
| ( sk3 != sk2 )
| ( emptyset != emptyset ) ),
inference(simp,[status(thm)],[275]) ).
thf(308,plain,
sk3 != sk2,
inference(simp,[status(thm)],[298]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ ( setadjoin @ B @ emptyset ) )
| ( A != sk2 )
| ( B != sk3 ) ),
inference(paramod_ordered,[status(thm)],[11,308]) ).
thf(321,plain,
! [A: $i] :
( ~ ( in @ A @ ( setadjoin @ sk3 @ emptyset ) )
| ( A != sk2 ) ),
inference(pattern_uni,[status(thm)],[320:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(322,plain,
~ ( in @ sk2 @ ( setadjoin @ sk3 @ emptyset ) ),
inference(simp,[status(thm)],[321]) ).
thf(324,plain,
~ ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ),
inference(rewrite,[status(thm)],[322,13]) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( in @ B @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) )
!= ( in @ sk2 @ ( setadjoin @ sk1 @ ( setadjoin @ sk2 @ emptyset ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,324]) ).
thf(330,plain,
$false,
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU652^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n017.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 : Sun May 19 16:41:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.08/1.06 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.23 % [INFO] Parsing done (165ms).
% 1.45/1.24 % [INFO] Running in sequential loop mode.
% 1.82/1.61 % [INFO] nitpick registered as external prover.
% 1.82/1.62 % [INFO] Scanning for conjecture ...
% 2.13/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.79 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.79 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.79 % [INFO] Type checking passed.
% 2.24/1.80 % [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 ...
% 6.45/3.05 % [INFO] Killing All external provers ...
% 6.45/3.05 % Time passed: 2532ms (effective reasoning time: 1805ms)
% 6.45/3.06 % 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)>
% 6.45/3.06 % Axioms used in derivation (0):
% 6.45/3.06 % No. of inferences in proof: 29
% 6.45/3.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2532 ms resp. 1805 ms w/o parsing
% 6.48/3.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.48/3.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------