TSTP Solution File: SEV260^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV260^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : Tue May 21 04:10:15 EDT 2024
% Result : Theorem 10.24s 3.63s
% Output : Refutation 10.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 94 ( 46 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 292 ( 35 ~; 8 |; 54 &; 144 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 109 ( 109 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 141 ( 51 ^ 84 !; 6 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(sk1_type,type,
sk1: ( a > $o ) > $o ).
thf(sk2_type,type,
sk2: ( b > $o ) > $o ).
thf(sk3_type,type,
sk3: a > b ).
thf(sk6_type,type,
sk6: b > $o ).
thf(sk7_type,type,
sk7: a > $o ).
thf(sk8_type,type,
sk8: a > $o ).
thf(1,conjecture,
! [A: ( a > $o ) > $o,B: ( b > $o ) > $o,C: a > b] :
( ( ! [D: a > $o] :
( ( D
= ( ^ [E: a] : $false ) )
=> ( A @ D ) )
& ! [D: a > $o] :
( ( D
= ( ^ [E: a] : ~ $false ) )
=> ( A @ D ) )
& ! [D: ( a > $o ) > $o,E: a > $o] :
( ( ! [F: a > $o] :
( ( D @ F )
=> ( A @ F ) )
& ( E
= ( ^ [F: a] :
? [G: a > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( A @ E ) )
& ! [D: a > $o,E: a > $o,F: a > $o] :
( ( ( A @ D )
& ( A @ E )
& ( F
= ( ^ [G: a] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( A @ F ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : $false ) )
=> ( B @ D ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : ~ $false ) )
=> ( B @ D ) )
& ! [D: ( b > $o ) > $o,E: b > $o] :
( ( ! [F: b > $o] :
( ( D @ F )
=> ( B @ F ) )
& ( E
= ( ^ [F: b] :
? [G: b > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( B @ E ) )
& ! [D: b > $o,E: b > $o,F: b > $o] :
( ( ( B @ D )
& ( B @ E )
& ( F
= ( ^ [G: b] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( B @ F ) )
& ! [D: b > $o] :
( ( B @ D )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ( A @ E ) ) ) )
=> ! [D: b > $o] :
( ! [E: b > $o] :
( ( E
= ( ^ [F: b] :
~ ( D @ F ) ) )
=> ( B @ E ) )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ! [F: a > $o] :
( ( F
= ( ^ [G: a] :
~ ( E @ G ) ) )
=> ( A @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCLOSED_THM1_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( a > $o ) > $o,B: ( b > $o ) > $o,C: a > b] :
( ( ! [D: a > $o] :
( ( D
= ( ^ [E: a] : $false ) )
=> ( A @ D ) )
& ! [D: a > $o] :
( ( D
= ( ^ [E: a] : ~ $false ) )
=> ( A @ D ) )
& ! [D: ( a > $o ) > $o,E: a > $o] :
( ( ! [F: a > $o] :
( ( D @ F )
=> ( A @ F ) )
& ( E
= ( ^ [F: a] :
? [G: a > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( A @ E ) )
& ! [D: a > $o,E: a > $o,F: a > $o] :
( ( ( A @ D )
& ( A @ E )
& ( F
= ( ^ [G: a] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( A @ F ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : $false ) )
=> ( B @ D ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : ~ $false ) )
=> ( B @ D ) )
& ! [D: ( b > $o ) > $o,E: b > $o] :
( ( ! [F: b > $o] :
( ( D @ F )
=> ( B @ F ) )
& ( E
= ( ^ [F: b] :
? [G: b > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( B @ E ) )
& ! [D: b > $o,E: b > $o,F: b > $o] :
( ( ( B @ D )
& ( B @ E )
& ( F
= ( ^ [G: b] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( B @ F ) )
& ! [D: b > $o] :
( ( B @ D )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ( A @ E ) ) ) )
=> ! [D: b > $o] :
( ! [E: b > $o] :
( ( E
= ( ^ [F: b] :
~ ( D @ F ) ) )
=> ( B @ E ) )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ! [F: a > $o] :
( ( F
= ( ^ [G: a] :
~ ( E @ G ) ) )
=> ( A @ F ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( a > $o ) > $o,B: ( b > $o ) > $o,C: a > b] :
( ( ! [D: a > $o] :
( ( D
= ( ^ [E: a] : $false ) )
=> ( A @ D ) )
& ! [D: a > $o] :
( ( D
= ( ^ [E: a] : $true ) )
=> ( A @ D ) )
& ! [D: ( a > $o ) > $o,E: a > $o] :
( ( ! [F: a > $o] :
( ( D @ F )
=> ( A @ F ) )
& ( E
= ( ^ [F: a] :
? [G: a > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( A @ E ) )
& ! [D: a > $o,E: a > $o,F: a > $o] :
( ( ( A @ D )
& ( A @ E )
& ( F
= ( ^ [G: a] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( A @ F ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : $false ) )
=> ( B @ D ) )
& ! [D: b > $o] :
( ( D
= ( ^ [E: b] : $true ) )
=> ( B @ D ) )
& ! [D: ( b > $o ) > $o,E: b > $o] :
( ( ! [F: b > $o] :
( ( D @ F )
=> ( B @ F ) )
& ( E
= ( ^ [F: b] :
? [G: b > $o] :
( ( D @ G )
& ( G @ F ) ) ) ) )
=> ( B @ E ) )
& ! [D: b > $o,E: b > $o,F: b > $o] :
( ( ( B @ D )
& ( B @ E )
& ( F
= ( ^ [G: b] :
( ( D @ G )
& ( E @ G ) ) ) ) )
=> ( B @ F ) )
& ! [D: b > $o] :
( ( B @ D )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ( A @ E ) ) ) )
=> ! [D: b > $o] :
( ! [E: b > $o] :
( ( E
= ( ^ [F: b] :
~ ( D @ F ) ) )
=> ( B @ E ) )
=> ! [E: a > $o] :
( ( E
= ( ^ [F: a] : ( D @ ( C @ F ) ) ) )
=> ! [F: a > $o] :
( ( F
= ( ^ [G: a] :
~ ( E @ G ) ) )
=> ( A @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [B: a > $o,A: b > $o] :
( ~ ( sk2 @ A )
| ( B
!= ( ^ [C: a] : ( A @ ( sk3 @ C ) ) ) )
| ( sk1 @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(26,plain,
! [B: a > $o,A: b > $o] :
( ( B
!= ( ^ [C: a] : ( A @ ( sk3 @ C ) ) ) )
| ~ ( sk2 @ A )
| ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(27,plain,
! [A: b > $o] :
( ~ ( sk2 @ A )
| ( sk1
@ ^ [B: a] : ( A @ ( sk3 @ B ) ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(11,plain,
~ ( sk1 @ sk8 ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( sk8
= ( ^ [A: a] :
~ ( sk7 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(21,plain,
( sk8
= ( ^ [A: a] :
~ ( sk7 @ A ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(54,plain,
~ ( sk1
@ ^ [A: a] :
~ ( sk7 @ A ) ),
inference(rewrite,[status(thm)],[11,21]) ).
thf(12,plain,
( sk7
= ( ^ [A: a] : ( sk6 @ ( sk3 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(32,plain,
( sk7
= ( ^ [A: a] : ( sk6 @ ( sk3 @ A ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(57,plain,
! [A: a] :
( ( sk7 @ A )
= ( sk6 @ ( sk3 @ A ) ) ),
inference(func_ext,[status(esa)],[32]) ).
thf(122,plain,
~ ( sk1
@ ^ [A: a] :
~ ( sk6 @ ( sk3 @ A ) ) ),
inference(rewrite,[status(thm)],[54,57]) ).
thf(160,plain,
! [A: b > $o] :
( ~ ( sk2 @ A )
| ( ( sk1
@ ^ [B: a] : ( A @ ( sk3 @ B ) ) )
!= ( sk1
@ ^ [B: a] :
~ ( sk6 @ ( sk3 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,122]) ).
thf(162,plain,
~ ( sk2
@ ^ [A: b] :
~ ( sk6 @ A ) ),
inference(pre_uni,[status(thm)],[160:[bind(A,$thf( ^ [B: b] : ~ ( sk6 @ B ) ))]]) ).
thf(18,plain,
! [A: b > $o] :
( ( A
!= ( ^ [B: b] :
~ ( sk6 @ B ) ) )
| ( sk2 @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(35,plain,
! [A: b > $o] :
( ( A
!= ( ^ [B: b] :
~ ( sk6 @ B ) ) )
| ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(36,plain,
( sk2
@ ^ [A: b] :
~ ( sk6 @ A ) ),
inference(simp,[status(thm)],[35]) ).
thf(171,plain,
~ $true,
inference(rewrite,[status(thm)],[162,36]) ).
thf(172,plain,
$false,
inference(simp,[status(thm)],[171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SEV260^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.15 % Command : run_Leo-III %s %d
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 18:53:54 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.89/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.10 % [INFO] Parsing done (175ms).
% 1.17/1.11 % [INFO] Running in sequential loop mode.
% 1.85/1.45 % [INFO] eprover registered as external prover.
% 1.85/1.45 % [INFO] cvc4 registered as external prover.
% 1.85/1.46 % [INFO] Scanning for conjecture ...
% 2.03/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.16/1.62 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.16/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.16/1.63 % [INFO] Type checking passed.
% 2.16/1.63 % [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 ...
% 10.24/3.63 % [INFO] Killing All external provers ...
% 10.24/3.63 % Time passed: 3136ms (effective reasoning time: 2505ms)
% 10.24/3.63 % 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)>
% 10.24/3.63 % Axioms used in derivation (0):
% 10.24/3.63 % No. of inferences in proof: 21
% 10.24/3.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3136 ms resp. 2505 ms w/o parsing
% 10.24/3.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.24/3.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------