TSTP Solution File: GEG002^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : GEG002^1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 : Mon May 20 19:56:58 EDT 2024
% Result : Theorem 19.10s 5.08s
% Output : Refutation 19.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of formulae : 101 ( 42 unt; 15 typ; 4 def)
% Number of atoms : 221 ( 70 equ; 0 cnn)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 466 ( 89 ~; 41 |; 24 &; 296 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 8 ^ 51 !; 9 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(reg_type,type,
reg: $tType ).
thf(c_type,type,
c: reg > reg > $o ).
thf(dc_type,type,
dc: reg > reg > $o ).
thf(dc_def,definition,
( dc
= ( ^ [A: reg,B: reg] :
~ ( c @ A @ B ) ) ) ).
thf(ec_type,type,
ec: reg > reg > $o ).
thf(ec_def,definition,
( ec
= ( ^ [A: reg,B: reg] :
( ( c @ A @ B )
& ~ ( o @ A @ B ) ) ) ) ).
thf(tpp_type,type,
tpp: reg > reg > $o ).
thf(tpp_def,definition,
( tpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(ntpp_type,type,
ntpp: reg > reg > $o ).
thf(ntpp_def,definition,
( ntpp
= ( ^ [A: reg,B: reg] :
( ( pp @ A @ B )
& ~ ? [C: reg] :
( ( ec @ C @ A )
& ( ec @ C @ B ) ) ) ) ) ).
thf(catalunya_type,type,
catalunya: reg ).
thf(france_type,type,
france: reg ).
thf(spain_type,type,
spain: reg ).
thf(paris_type,type,
paris: reg ).
thf(sk1_type,type,
sk1: reg ).
thf(sk2_type,type,
sk2: reg ).
thf(sk5_type,type,
sk5: reg > reg ).
thf(sk6_type,type,
sk6: reg > reg ).
thf(sk9_type,type,
sk9: reg ).
thf(5,axiom,
tpp @ catalunya @ spain,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(14,plain,
( ! [A: reg] :
( ( c @ A @ catalunya )
=> ( c @ A @ spain ) )
& ~ ! [A: reg] :
( ( c @ A @ spain )
=> ( c @ A @ catalunya ) )
& ? [A: reg] :
( ( c @ A @ catalunya )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ catalunya ) ) )
& ( c @ A @ spain )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ spain ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [A: reg] :
( ( c @ ( sk5 @ A ) @ A )
| ( c @ ( sk6 @ A ) @ A ) ),
inference(cnf,[status(esa)],[14]) ).
thf(29,plain,
! [A: reg] :
( ( c @ ( sk5 @ A ) @ A )
| ( c @ ( sk6 @ A ) @ A ) ),
inference(simp,[status(thm)],[17]) ).
thf(18,plain,
c @ sk2 @ catalunya,
inference(cnf,[status(esa)],[14]) ).
thf(4,axiom,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_symmetric) ).
thf(12,plain,
! [A: reg,B: reg] :
( ( c @ A @ B )
=> ( c @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( c @ B @ A ) ),
inference(cnf,[status(esa)],[12]) ).
thf(115,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk2 @ catalunya )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[18,13]) ).
thf(116,plain,
c @ catalunya @ sk2,
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk2 )),bind(B,$thf( catalunya ))]]) ).
thf(21,plain,
c @ sk1 @ spain,
inference(cnf,[status(esa)],[14]) ).
thf(1,conjecture,
( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ( dc @ catalunya @ paris )
& ( dc @ spain @ paris ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( ~ ( c @ catalunya @ paris )
& ~ ( c @ spain @ paris ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
( ( c @ catalunya @ paris )
| ( c @ spain @ paris ) ),
inference(cnf,[status(esa)],[8]) ).
thf(7,axiom,
ntpp @ paris @ france,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(42,plain,
( ! [A: reg] :
( ( c @ A @ paris )
=> ( c @ A @ france ) )
& ~ ! [A: reg] :
( ( c @ A @ france )
=> ( c @ A @ paris ) )
& ~ ? [A: reg] :
( ( c @ A @ paris )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ paris ) ) )
& ( c @ A @ france )
& ~ ? [B: reg] :
( ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ A ) )
& ! [C: reg] :
( ( c @ C @ B )
=> ( c @ C @ france ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(49,plain,
c @ sk9 @ france,
inference(cnf,[status(esa)],[42]) ).
thf(47,plain,
~ ( c @ sk9 @ paris ),
inference(cnf,[status(esa)],[42]) ).
thf(93,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk9 @ france ) ),
inference(paramod_ordered,[status(thm)],[49,47]) ).
thf(95,plain,
( ( sk9 != sk9 )
| ( paris != france ) ),
inference(simp,[status(thm)],[93]) ).
thf(96,plain,
paris != france,
inference(simp,[status(thm)],[95]) ).
thf(69,plain,
( ( c @ catalunya @ paris )
| ( ( c @ sk9 @ paris )
!= ( c @ spain @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[9,47]) ).
thf(72,plain,
( ( c @ catalunya @ paris )
| ( sk9 != spain )
| ( paris != paris ) ),
inference(simp,[status(thm)],[69]) ).
thf(75,plain,
( ( c @ catalunya @ paris )
| ( sk9 != spain ) ),
inference(simp,[status(thm)],[72]) ).
thf(78,plain,
( ( sk9 != spain )
| ( ( c @ sk9 @ paris )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[75,47]) ).
thf(80,plain,
( ( sk9 != spain )
| ( sk9 != catalunya )
| ( paris != paris ) ),
inference(simp,[status(thm)],[78]) ).
thf(81,plain,
( ( sk9 != spain )
| ( sk9 != catalunya ) ),
inference(simp,[status(thm)],[80]) ).
thf(24,plain,
c @ sk2 @ spain,
inference(cnf,[status(esa)],[14]) ).
thf(107,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk2 @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,13]) ).
thf(108,plain,
c @ spain @ sk2,
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( sk2 )),bind(B,$thf( spain ))]]) ).
thf(129,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( ( c @ B @ A )
!= ( c @ sk9 @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[13,47]) ).
thf(130,plain,
~ ( c @ paris @ sk9 ),
inference(pattern_uni,[status(thm)],[129:[bind(A,$thf( paris )),bind(B,$thf( sk9 ))]]) ).
thf(111,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk1 @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(112,plain,
c @ spain @ sk1,
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( sk1 )),bind(B,$thf( spain ))]]) ).
thf(3,axiom,
! [A: reg] : ( c @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_reflexive) ).
thf(10,plain,
! [A: reg] : ( c @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: reg] : ( c @ A @ A ),
inference(cnf,[status(esa)],[10]) ).
thf(83,plain,
! [A: reg] :
( ( c @ A @ A )
!= ( c @ sk9 @ paris ) ),
inference(paramod_ordered,[status(thm)],[11,47]) ).
thf(85,plain,
! [A: reg] :
( ( A != sk9 )
| ( A != paris ) ),
inference(simp,[status(thm)],[83]) ).
thf(87,plain,
sk9 != paris,
inference(simp,[status(thm)],[85]) ).
thf(6,axiom,
ec @ spain @ france,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(36,plain,
( ( c @ spain @ france )
& ~ ? [A: reg] :
( ! [B: reg] :
( ( c @ B @ A )
=> ( c @ B @ spain ) )
& ! [B: reg] :
( ( c @ B @ A )
=> ( c @ B @ france ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(121,plain,
! [B: reg,A: reg] :
( ( sk9 != spain )
| ( c @ B @ A )
| ( ( c @ catalunya @ paris )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[75,13]) ).
thf(122,plain,
( ( sk9 != spain )
| ( c @ paris @ catalunya ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( catalunya )),bind(B,$thf( paris ))]]) ).
thf(16,plain,
~ ( c @ sk1 @ catalunya ),
inference(cnf,[status(esa)],[14]) ).
thf(54,plain,
( ( c @ sk2 @ catalunya )
!= ( c @ sk1 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[18,16]) ).
thf(55,plain,
( ( sk2 != sk1 )
| ( catalunya != catalunya ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
sk2 != sk1,
inference(simp,[status(thm)],[55]) ).
thf(41,plain,
c @ spain @ france,
inference(cnf,[status(esa)],[36]) ).
thf(127,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ sk9 @ france )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[49,13]) ).
thf(128,plain,
c @ france @ sk9,
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( sk9 )),bind(B,$thf( france ))]]) ).
thf(23,plain,
! [A: reg] :
( ~ ( c @ A @ catalunya )
| ( c @ A @ spain ) ),
inference(cnf,[status(esa)],[14]) ).
thf(243,plain,
! [A: reg] :
( ( sk9 != spain )
| ( c @ A @ spain )
| ( ( c @ paris @ catalunya )
!= ( c @ A @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[122,23]) ).
thf(244,plain,
( ( sk9 != spain )
| ( c @ paris @ spain ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( paris ))]]) ).
thf(57,plain,
( ( c @ sk1 @ spain )
!= ( c @ sk1 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[21,16]) ).
thf(58,plain,
( ( sk1 != sk1 )
| ( spain != catalunya ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
spain != catalunya,
inference(simp,[status(thm)],[58]) ).
thf(117,plain,
! [B: reg,A: reg] :
( ~ ( c @ A @ B )
| ( ( c @ B @ A )
!= ( c @ sk1 @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[13,16]) ).
thf(118,plain,
~ ( c @ catalunya @ sk1 ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( catalunya )),bind(B,$thf( sk1 ))]]) ).
thf(82,plain,
! [A: reg] :
( ( c @ A @ A )
!= ( c @ sk1 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[11,16]) ).
thf(84,plain,
! [A: reg] :
( ( A != sk1 )
| ( A != catalunya ) ),
inference(simp,[status(thm)],[82]) ).
thf(86,plain,
sk1 != catalunya,
inference(simp,[status(thm)],[84]) ).
thf(61,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk2 @ catalunya ) ),
inference(paramod_ordered,[status(thm)],[18,47]) ).
thf(63,plain,
( ( sk9 != sk2 )
| ( paris != catalunya ) ),
inference(simp,[status(thm)],[61]) ).
thf(65,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk2 @ spain ) ),
inference(paramod_ordered,[status(thm)],[24,47]) ).
thf(67,plain,
( ( sk9 != sk2 )
| ( paris != spain ) ),
inference(simp,[status(thm)],[65]) ).
thf(159,plain,
( ( sk9 != spain )
| ( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ paris ) ) ),
inference(paramod_ordered,[status(thm)],[75,118]) ).
thf(168,plain,
( ( sk9 != spain )
| ( catalunya != catalunya )
| ( sk1 != paris ) ),
inference(simp,[status(thm)],[159]) ).
thf(177,plain,
( ( sk9 != spain )
| ( sk1 != paris ) ),
inference(simp,[status(thm)],[168]) ).
thf(238,plain,
! [B: reg,A: reg] :
( ( c @ B @ spain )
| ( ( c @ A @ A )
!= ( c @ B @ catalunya ) ) ),
inference(paramod_ordered,[status(thm)],[11,23]) ).
thf(239,plain,
c @ catalunya @ spain,
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( catalunya )),bind(B,$thf( catalunya ))]]) ).
thf(305,plain,
( ( c @ catalunya @ sk1 )
!= ( c @ catalunya @ spain ) ),
inference(paramod_ordered,[status(thm)],[239,118]) ).
thf(312,plain,
( ( catalunya != catalunya )
| ( sk1 != spain ) ),
inference(simp,[status(thm)],[305]) ).
thf(314,plain,
sk1 != spain,
inference(simp,[status(thm)],[312]) ).
thf(303,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ catalunya @ spain )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[239,13]) ).
thf(304,plain,
c @ spain @ catalunya,
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( catalunya )),bind(B,$thf( spain ))]]) ).
thf(125,plain,
! [B: reg,A: reg] :
( ( c @ B @ A )
| ( ( c @ spain @ france )
!= ( c @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[41,13]) ).
thf(126,plain,
c @ france @ spain,
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( spain )),bind(B,$thf( france ))]]) ).
thf(60,plain,
( ( c @ sk9 @ paris )
!= ( c @ sk1 @ spain ) ),
inference(paramod_ordered,[status(thm)],[21,47]) ).
thf(62,plain,
( ( sk9 != sk1 )
| ( paris != spain ) ),
inference(simp,[status(thm)],[60]) ).
thf(1754,plain,
$false,
inference(e,[status(thm)],[14,29,116,21,9,96,81,108,130,112,87,36,122,10,56,42,24,13,41,128,244,59,118,12,49,86,63,18,67,177,16,11,314,304,23,8,75,239,126,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEG002^1 : TPTP v8.2.0. Released v4.1.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat May 18 21:56:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.30/1.20 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.72/1.41 % [INFO] Parsing done (206ms).
% 1.72/1.43 % [INFO] Running in sequential loop mode.
% 2.45/1.90 % [INFO] eprover registered as external prover.
% 2.45/1.90 % [INFO] cvc4 registered as external prover.
% 2.45/1.91 % [INFO] Scanning for conjecture ...
% 2.83/2.06 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.03/2.10 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.03/2.11 % [INFO] Problem is higher-order (TPTP THF).
% 3.03/2.11 % [INFO] Type checking passed.
% 3.08/2.12 % [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 ...
% 19.10/5.07 % External prover 'e' found a proof!
% 19.10/5.07 % [INFO] Killing All external provers ...
% 19.10/5.07 % Time passed: 4518ms (effective reasoning time: 3640ms)
% 19.10/5.07 % 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)>
% 19.10/5.08 % Axioms used in derivation (5): c_symmetric, ax1, ax2, ax3, c_reflexive
% 19.10/5.08 % No. of inferences in proof: 82
% 19.10/5.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4518 ms resp. 3640 ms w/o parsing
% 19.10/5.15 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.10/5.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------