TSTP Solution File: LCL691^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : LCL691^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n001.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 11:19:08 EDT 2024
% Result : Theorem 63.62s 9.92s
% Output : Refutation 63.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 24 unt; 0 typ; 7 def)
% Number of atoms : 113 ( 14 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 320 ( 36 ~; 49 |; 0 &; 227 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 73 ( 15 ^ 58 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(mimpl_type,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimpl_def,definition,
( mimpl
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [A: $i > $i > $o,B: $i > $o,C: $i] :
! [D: $i] :
( ( A @ C @ D )
=> ( B @ D ) ) ) ) ).
thf(individuals_type,type,
individuals: $tType ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(reli_type,type,
reli: $i > $i > $o ).
thf(relr_type,type,
relr: $i > $i > $o ).
thf(cs4_atom_type,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(cs4_atom_def,definition,
( cs4_atom
= ( mbox @ reli ) ) ).
thf(cs4_impl_type,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(cs4_impl_def,definition,
( cs4_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ) ).
thf(cs4_box_type,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(cs4_box_def,definition,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ) ).
thf(cs4_valid_type,type,
cs4_valid: ( $i > $o ) > $o ).
thf(cs4_valid_def,definition,
cs4_valid = mvalid ).
thf(sk1_type,type,
sk1: $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i > ( $i > $o ) > $i ).
thf(sk6_type,type,
sk6: $i > ( $i > $o ) > $i ).
thf(4,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ relr @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_r) ).
thf(16,plain,
! [A: $i > $o,B: $i] :
( ~ ! [C: $i] :
( ( relr @ B @ C )
=> ( A @ C ) )
| ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [B: $i,A: $i > $o] :
( ( relr @ B @ ( sk6 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(3,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom_i) ).
thf(13,plain,
! [A: $i > $o,B: $i] :
( ~ ! [C: $i] :
( ( reli @ B @ C )
=> ( A @ C ) )
| ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
! [B: $i,A: $i > $o] :
( ( reli @ B @ ( sk5 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk5 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(35,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ~ ( ( B
@ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) )
| ( C
@ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[15:[bind(A,$thf( ^ [E: $i] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(54,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(56,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) ) ),
inference(simp,[status(thm)],[54]) ).
thf(1,conjecture,
! [A: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_atom @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cs4_refl) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_atom @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i > $o,B: $i,C: $i] :
( ( reli @ B @ C )
=> ( ~ ! [D: $i] :
( ( reli @ C @ D )
=> ! [E: $i] :
( ( relr @ D @ E )
=> ! [F: $i] :
( ( reli @ E @ F )
=> ( A @ F ) ) ) )
| ! [D: $i] :
( ( reli @ C @ D )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
reli @ sk3 @ sk4,
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( reli @ sk3 @ A )
| ~ ( relr @ A @ B )
| ~ ( reli @ B @ C )
| ( sk1 @ C ) ),
inference(cnf,[status(esa)],[8]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( reli @ sk3 @ A )
| ~ ( relr @ A @ B )
| ( sk1 @ C )
| ( ( reli @ sk3 @ sk4 )
!= ( reli @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[10,11]) ).
thf(68,plain,
! [A: $i] :
( ~ ( reli @ sk3 @ A )
| ~ ( relr @ A @ sk3 )
| ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(9,plain,
~ ( sk1 @ sk4 ),
inference(cnf,[status(esa)],[8]) ).
thf(5939,plain,
! [A: $i] :
( ~ ( reli @ sk3 @ A )
| ~ ( relr @ A @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[68,9]) ).
thf(5940,plain,
! [A: $i] :
( ~ ( reli @ sk3 @ A )
| ~ ( relr @ A @ sk3 ) ),
inference(simp,[status(thm)],[5939]) ).
thf(5954,plain,
! [A: $i] :
( ~ ( relr @ A @ sk3 )
| ( ( reli @ sk3 @ sk4 )
!= ( reli @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,5940]) ).
thf(5955,plain,
~ ( relr @ sk4 @ sk3 ),
inference(pattern_uni,[status(thm)],[5954:[bind(A,$thf( sk4 ))]]) ).
thf(7835,plain,
! [C: $i > $o,B: $i > $o,A: $i] :
( ( C @ A )
| ~ ( C
@ ( sk5 @ A
@ ^ [D: $i] :
( ( B @ D )
| ( C @ D ) ) ) )
| ( ( B @ A )
!= ( relr @ sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[56,5955]) ).
thf(7938,plain,
! [A: $i > $o] :
( ( A @ sk3 )
| ~ ( A
@ ( sk5 @ sk3
@ ^ [B: $i] :
( ( relr @ sk4 @ B )
| ( A @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[7835:[bind(A,$thf( sk3 )),bind(B,$thf( relr @ sk4 )),bind(C,$thf( C ))]]) ).
thf(8161,plain,
! [A: $i > $o] :
( ( A @ sk3 )
| ~ ( A
@ ( sk5 @ sk3
@ ^ [B: $i] :
( ( relr @ sk4 @ B )
| ( A @ B ) ) ) ) ),
inference(simp,[status(thm)],[7938]) ).
thf(8705,plain,
! [C: $i > $o,B: $i,A: $i > $o] :
( ( A @ B )
| ( C @ sk3 )
| ( ( reli @ B @ ( sk5 @ B @ A ) )
!= ( C
@ ( sk5 @ sk3
@ ^ [D: $i] :
( ( relr @ sk4 @ D )
| ( C @ D ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,8161]) ).
thf(8767,plain,
( ( relr @ sk4 @ sk3 )
| ( reli @ sk3 @ sk3 )
| ( reli @ sk3 @ sk3 ) ),
inference(pre_uni,[status(thm)],[8705:[bind(A,$thf( ^ [D: $i] : ( ( relr @ sk4 @ D ) | ( reli @ sk3 @ D ) ) )),bind(B,$thf( sk3 )),bind(C,$thf( reli @ sk3 ))]]) ).
thf(8841,plain,
( ( reli @ sk3 @ sk3 )
| ( relr @ sk4 @ sk3 )
| ( reli @ sk3 @ sk3 ) ),
inference(cnf,[status(esa)],[8767]) ).
thf(8842,plain,
( ( reli @ sk3 @ sk3 )
| ( relr @ sk4 @ sk3 ) ),
inference(simp,[status(thm)],[8841]) ).
thf(9503,plain,
( ( reli @ sk3 @ sk3 )
| $false ),
inference(rewrite,[status(thm)],[8842,5955]) ).
thf(9504,plain,
reli @ sk3 @ sk3,
inference(simp,[status(thm)],[9503]) ).
thf(9526,plain,
! [A: $i] :
( ~ ( relr @ A @ sk3 )
| ( ( reli @ sk3 @ sk3 )
!= ( reli @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9504,5940]) ).
thf(9527,plain,
~ ( relr @ sk3 @ sk3 ),
inference(pattern_uni,[status(thm)],[9526:[bind(A,$thf( sk3 ))]]) ).
thf(9579,plain,
! [B: $i,A: $i > $o] :
( ( relr @ B @ ( sk6 @ B @ A ) )
| ( ( A @ B )
!= ( relr @ sk3 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[17,9527]) ).
thf(9624,plain,
relr @ sk3 @ ( sk6 @ sk3 @ ( relr @ sk3 ) ),
inference(pre_uni,[status(thm)],[9579:[bind(A,$thf( relr @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(18,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk6 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(10687,plain,
! [B: $i,A: $i > $o] :
( ( A @ B )
| ( ( relr @ sk3 @ ( sk6 @ sk3 @ ( relr @ sk3 ) ) )
!= ( A @ ( sk6 @ B @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[9624,18]) ).
thf(10713,plain,
relr @ sk3 @ sk3,
inference(pre_uni,[status(thm)],[10687:[bind(A,$thf( relr @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(10743,plain,
$false,
inference(rewrite,[status(thm)],[10713,9527]) ).
thf(10744,plain,
$false,
inference(simp,[status(thm)],[10743]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL691^1 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n001.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 : Sat Jun 22 15:16:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.02 % [INFO] Parsing done (142ms).
% 1.38/1.03 % [INFO] Running in sequential loop mode.
% 1.90/1.25 % [INFO] nitpick registered as external prover.
% 1.90/1.25 % [INFO] Scanning for conjecture ...
% 2.14/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.14/1.36 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.14/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.37 % [INFO] Type checking passed.
% 2.14/1.37 % [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 ...
% 63.62/9.87 % [INFO] Killing All external provers ...
% 63.62/9.92 % Time passed: 9340ms (effective reasoning time: 8845ms)
% 63.62/9.92 % 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)>
% 63.62/9.92 % Axioms used in derivation (2): refl_axiom_r, refl_axiom_i
% 63.62/9.92 % No. of inferences in proof: 40
% 63.62/9.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9340 ms resp. 8845 ms w/o parsing
% 63.81/9.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 63.81/9.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------