TSTP Solution File: SEV082^5 by Leo-III---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV082^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n018.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 3.48s 2.34s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 54 equ; 32 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 174 ( 18 ~; 20 |; 9 &; 124 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 24 ^ 15 !; 3 ?; 42 :)
% 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(sk3_type,type,
sk3: ( ( $i > $o ) > ( $i > $o ) > $o ) > $i > $o ).
thf(sk4_type,type,
sk4: ( ( $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 ) ) )
| $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM120_4_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 ) ) )
| $false ),
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 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk3 @ A ) @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(14,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(15,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(6,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ ( sk2 @ A ) @ ( sk3 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
= ( sk3 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[6:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(10,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(11,plain,
( ( sk3 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(18,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(rewrite,[status(thm)],[15,11]) ).
thf(4,plain,
! [A: ( $i > $o ) > ( $i > $o ) > $o] :
( ( A
@ ^ [B: $i] : $true
@ ^ [B: $i] : $false )
| ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ~ ( A @ ( sk2 @ A ) @ ( sk4 @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
( ( ( ^ [A: $i] : $true )
= ( ^ [A: $i] : $false ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk2 @ ( (=) @ ( $i > $o ) ) )
!= ( sk4 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(replace_andrewseq,[status(thm)],[4:[bind(A,$thf( (=) @ ( $i > $o ) ))]]) ).
thf(12,plain,
( ( ( ^ [A: $i] : $false )
= ( ^ [A: $i] : $true ) )
| ( ( sk1 @ ( (=) @ ( $i > $o ) ) )
!= ( sk1 @ ( (=) @ ( $i > $o ) ) ) )
| ( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
( ( sk4 @ ( (=) @ ( $i > $o ) ) )
!= ( sk2 @ ( (=) @ ( $i > $o ) ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(19,plain,
$false,
inference(simplifyReflect,[status(thm)],[18,13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEV082^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.10 % Command : run_Leo-III %s %d THM
% 0.10/0.30 % Computer : n018.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 21 19:03:54 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.99/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.17 % [INFO] Parsing done (167ms).
% 1.18/1.18 % [INFO] Running in sequential loop mode.
% 1.93/1.56 % [INFO] eprover registered as external prover.
% 1.93/1.57 % [INFO] Scanning for conjecture ...
% 2.11/1.66 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.70 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.70 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.71 % [INFO] Type checking passed.
% 2.21/1.71 % [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 ...
% 3.48/2.34 % [INFO] Killing All external provers ...
% 3.48/2.34 % Time passed: 1851ms (effective reasoning time: 1152ms)
% 3.48/2.34 % 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)>
% 3.48/2.34 % Axioms used in derivation (0):
% 3.48/2.34 % No. of inferences in proof: 17
% 3.48/2.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1851 ms resp. 1152 ms w/o parsing
% 3.83/2.46 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/2.46 % [INFO] Killing All external provers ...
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