TSTP Solution File: SEV087^5 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n024.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 Jun 24 15:58:10 EDT 2024
% Result : Theorem 3.82s 2.20s
% Output : Refutation 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 64 ( 29 equ; 16 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 131 ( 12 ~; 10 |; 15 &; 88 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 12 ^ 19 !; 3 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_type,type,
sk1: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk2_type,type,
sk2: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk4_type,type,
sk4: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk5_type,type,
sk5: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk6_type,type,
sk6: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(1,conjecture,
? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM120H_pme) ).
thf(2,negated_conjecture,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ~ ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
& ! [B: $i > $o] : ( A @ B @ B )
& ! [B: $i > $o,C: $i > $o,D: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) )
& ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B @ C )
& ( A @ C @ B ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) )
| ( A @ ( sk6 @ A ) @ ( sk5 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[10:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(23,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(24,plain,
( ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk6 @ ( (=) @ ( $i > $o ) ) )
= ( sk5 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(54,plain,
$false,
inference(e,[status(thm)],[3,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SEV087^5 : TPTP v8.2.0. Released v4.0.0.
% 0.05/0.09 % Command : run_Leo-III %s %d THM
% 0.08/0.29 % Computer : n024.cluster.edu
% 0.08/0.29 % Model : x86_64 x86_64
% 0.08/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.29 % Memory : 8042.1875MB
% 0.08/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.29 % CPULimit : 300
% 0.08/0.29 % WCLimit : 300
% 0.08/0.29 % DateTime : Fri Jun 21 19:17:40 EDT 2024
% 0.08/0.29 % CPUTime :
% 1.11/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.09 % [INFO] Parsing done (114ms).
% 1.35/1.10 % [INFO] Running in sequential loop mode.
% 1.76/1.36 % [INFO] eprover registered as external prover.
% 1.76/1.36 % [INFO] Scanning for conjecture ...
% 2.03/1.44 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.48 % [INFO] Type checking passed.
% 2.08/1.48 % [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 ...
% 3.82/2.19 % External prover 'e' found a proof!
% 3.82/2.20 % [INFO] Killing All external provers ...
% 3.82/2.20 % Time passed: 1671ms (effective reasoning time: 1097ms)
% 3.82/2.20 % 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)>
% 3.82/2.20 % Axioms used in derivation (0):
% 3.82/2.20 % No. of inferences in proof: 8
% 3.82/2.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1671 ms resp. 1097 ms w/o parsing
% 3.82/2.24 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.82/2.24 % [INFO] Killing All external provers ...
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