TSTP Solution File: SEV121^5 by Leo-III---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEV121^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 04:10:00 EDT 2024
% Result : Theorem 6.70s 2.79s
% Output : Refutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 13 unt; 4 typ; 0 def)
% Number of atoms : 47 ( 38 equ; 4 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 238 ( 32 ~; 43 |; 0 &; 154 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 47 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 69 ( 36 ^ 33 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i > $o ).
thf(sk4_type,type,
sk4: ( $i > $i > $o ) > $i ).
thf(1,conjecture,
( ( (=) @ $i )
= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM47C_pme) ).
thf(2,negated_conjecture,
( ( (=) @ $i )
!= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( (=) @ $i )
!= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( (=) @ $i )
!= ( ^ [A: $i,B: $i] :
! [C: $i > $i > $o] :
( ! [D: $i] : ( C @ D @ D )
=> ( C @ A @ B ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( sk1 = sk2 )
!= ( ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(7,plain,
( ( sk1 = sk2 )
| ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( sk2 = sk1 )
| ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
! [A: $i > $i > $o] :
( ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 )
| ( sk2 = sk1 ) ),
inference(cnf,[status(esa)],[9]) ).
thf(6,plain,
( ( sk1 != sk2 )
| ~ ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk2 != sk1 )
| ~ ! [A: $i > $i > $o] :
( ! [B: $i] : ( A @ B @ B )
=> ( A @ sk1 @ sk2 ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i] :
( ( sk3 @ A @ A )
| ( sk2 != sk1 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ~ ( sk3 @ sk1 @ sk2 )
| ( sk2 != sk1 ) ),
inference(cnf,[status(esa)],[8]) ).
thf(13,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( ( sk3 @ A @ A )
!= ( sk3 @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,10]) ).
thf(14,plain,
! [A: $i] :
( ( sk2 != sk1 )
| ( A != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[13]) ).
thf(15,plain,
sk2 != sk1,
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
! [A: $i > $i > $o] :
( ~ ( A @ ( sk4 @ A ) @ ( sk4 @ A ) )
| ( A @ sk1 @ sk2 ) ),
inference(simplifyReflect,[status(thm)],[12,15]) ).
thf(20,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ~ ( ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( B
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) )
| ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 ) ),
inference(prim_subst,[status(thm)],[16:[bind(A,$thf( ^ [D: $i] : ^ [E: $i] : ( ( B @ D @ E ) | ( C @ D @ E ) ) ))]]) ).
thf(25,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 )
| ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(27,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ sk1 @ sk2 )
| ( B @ sk1 @ sk2 )
| ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) ) ),
inference(simp,[status(thm)],[25]) ).
thf(36,plain,
! [B: $i > $i > $o,A: $i > $i > $o] :
( ( A @ sk1 @ sk2 )
| ~ ( A
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) )
@ ( sk4
@ ^ [C: $i,D: $i] :
( ( A @ C @ D )
| ( B @ C @ D ) ) ) )
| ( ( B @ sk1 @ sk2 )
!= ( A @ sk1 @ sk2 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(63,plain,
! [A: $i > $i > $o] :
( ( sk1 = sk2 )
| ( ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) )
!= ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) )
| ( ( A @ sk1 @ sk2 )
!= ( sk1 = sk2 ) )
| ~ $true ),
inference(replace_andrewseq,[status(thm)],[36:[bind(A,$thf( (=) @ $i ))]]) ).
thf(74,plain,
! [A: $i > $i > $o] :
( ( sk2 = sk1 )
| ( ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) )
!= ( sk4
@ ^ [B: $i,C: $i] :
( ( B = C )
| ( A @ B @ C ) ) ) )
| ( ( A @ sk1 @ sk2 )
!= ( sk1 = sk2 ) )
| ~ $true ),
inference(lifteq,[status(thm)],[63]) ).
thf(77,plain,
( ~ $true
| ( sk2 = sk1 ) ),
inference(pre_uni,[status(thm)],[74:[bind(A,$thf( ^ [B: $i] : ^ [C: $i] : ( sk1 = sk2 ) ))]]) ).
thf(105,plain,
sk2 = sk1,
inference(simp,[status(thm)],[77]) ).
thf(149,plain,
$false,
inference(simplifyReflect,[status(thm)],[105,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEV121^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 18:26:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 1.00/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.11 % [INFO] Parsing done (153ms).
% 1.26/1.12 % [INFO] Running in sequential loop mode.
% 1.83/1.49 % [INFO] eprover registered as external prover.
% 1.83/1.49 % [INFO] cvc4 registered as external prover.
% 1.83/1.50 % [INFO] Scanning for conjecture ...
% 1.98/1.58 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.98/1.60 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.98/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 1.98/1.61 % [INFO] Type checking passed.
% 1.98/1.61 % [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 ...
% 6.70/2.78 % [INFO] Killing All external provers ...
% 6.70/2.79 % Time passed: 2303ms (effective reasoning time: 1654ms)
% 6.70/2.79 % 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)>
% 6.70/2.79 % Axioms used in derivation (0):
% 6.70/2.79 % No. of inferences in proof: 25
% 6.70/2.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2303 ms resp. 1654 ms w/o parsing
% 6.70/2.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.70/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------