TSTP Solution File: SYO049^1 by Leo-III-SAT---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n025.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 20:54:04 EDT 2024
% Result : Theorem 4.39s 1.94s
% Output : Refutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 10 unt; 0 typ; 5 def)
% Number of atoms : 162 ( 15 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 400 ( 111 ~; 91 |; 0 &; 198 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 12 con; 0-3 aty)
% Number of variables : 55 ( 13 ^ 42 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_def,definition,
( mor
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: $i > $o,B: $i > $o] : ( mand @ ( mimplies @ A @ B ) @ ( mimplies @ B @ A ) ) ) ) ).
thf(mforall_prop_type,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(mforall_prop_def,definition,
( mforall_prop
= ( ^ [A: ( $i > $o ) > $i > $o,B: $i] :
! [C: $i > $o] : ( A @ C @ B ) ) ) ).
thf(mdia_type,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [A: $i > $i > $o,B: $i > $o] : ( mnot @ ( mbox @ A @ ( mnot @ B ) ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $o ).
thf(sk5_type,type,
sk5: $i > $o ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i > $i > $o ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i > $o ).
thf(sk10_type,type,
sk10: $i > $o ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mequiv @ ( mdia @ A @ ( mor @ B @ C ) ) @ ( mor @ ( mdia @ A @ B ) @ ( mdia @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( mvalid
@ ( mforall_prop
@ ^ [B: $i > $o] :
( mforall_prop
@ ^ [C: $i > $o] : ( mequiv @ ( mdia @ A @ ( mor @ B @ C ) ) @ ( mor @ ( mdia @ A @ B ) @ ( mdia @ A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
~ ( ~ ( ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ( C @ E )
| ( D @ E ) ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E ) ) )
| ~ ( ~ ( ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E ) ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ~ ( ~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
( ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ( C @ E )
| ( D @ E ) ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E ) ) )
| ~ ! [A: $i > $i > $o,B: $i,C: $i > $o,D: $i > $o] :
( ~ ( ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( C @ E ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( D @ E ) ) )
| ~ ! [E: $i] :
( ~ ( A @ B @ E )
| ~ ( ( C @ E )
| ( D @ E ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(10,plain,
( ( sk4 @ sk6 )
| ( sk5 @ sk6 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
( ~ sk1
| ( sk7 @ sk8 @ sk11 )
| ( sk7 @ sk8 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(12,plain,
( ~ sk1
| ( sk9 @ sk11 )
| ( sk10 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
( ~ sk1
| ( sk9 @ sk11 )
| ( sk7 @ sk8 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ~ ( sk10 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ~ ( sk10 @ A ) ),
inference(simp,[status(thm)],[14]) ).
thf(24,plain,
! [A: $i] :
( ~ sk1
| ( sk9 @ sk11 )
| ~ ( sk10 @ A )
| ( ( sk7 @ sk8 @ sk12 )
!= ( sk7 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7,16]) ).
thf(25,plain,
( ~ sk1
| ( sk9 @ sk11 )
| ~ ( sk10 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( sk12 ))]]) ).
thf(42,plain,
( ~ sk1
| ( sk9 @ sk11 )
| ( ( sk10 @ sk12 )
!= ( sk10 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[12,25]) ).
thf(43,plain,
( ~ sk1
| ( sk9 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[42:[]]) ).
thf(6,plain,
( ~ sk1
| ( sk7 @ sk8 @ sk11 )
| ( sk10 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(5,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ~ ( sk9 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(15,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ~ ( sk9 @ A ) ),
inference(simp,[status(thm)],[5]) ).
thf(18,plain,
! [A: $i] :
( ~ sk1
| ( sk10 @ sk12 )
| ~ ( sk9 @ A )
| ( ( sk7 @ sk8 @ sk11 )
!= ( sk7 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,15]) ).
thf(19,plain,
( ~ sk1
| ( sk10 @ sk12 )
| ~ ( sk9 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( sk11 ))]]) ).
thf(46,plain,
( ~ sk1
| ( sk10 @ sk12 )
| ( ( sk9 @ sk11 )
!= ( sk9 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[43,19]) ).
thf(47,plain,
( ~ sk1
| ( sk10 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[46:[]]) ).
thf(50,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ( ( sk10 @ sk12 )
!= ( sk10 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[47,16]) ).
thf(51,plain,
( ~ sk1
| ~ ( sk7 @ sk8 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk12 ))]]) ).
thf(55,plain,
( ~ sk1
| ( sk7 @ sk8 @ sk11 )
| ( ( sk7 @ sk8 @ sk12 )
!= ( sk7 @ sk8 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[13,51]) ).
thf(56,plain,
( ~ sk1
| ( sk7 @ sk8 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[55:[]]) ).
thf(48,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk7 @ sk8 @ A )
| ( ( sk9 @ sk11 )
!= ( sk9 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[43,15]) ).
thf(49,plain,
( ~ sk1
| ~ ( sk7 @ sk8 @ sk11 ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk11 ))]]) ).
thf(65,plain,
( ~ sk1
| ( ( sk7 @ sk8 @ sk11 )
!= ( sk7 @ sk8 @ sk11 ) ) ),
inference(paramod_ordered,[status(thm)],[56,49]) ).
thf(66,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[65:[]]) ).
thf(78,plain,
( ( sk4 @ sk6 )
| ( sk5 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[10,66]) ).
thf(79,plain,
( ( sk4 @ sk6 )
| ( sk5 @ sk6 ) ),
inference(simp,[status(thm)],[78]) ).
thf(9,plain,
( ( sk2 @ sk3 @ sk6 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(76,plain,
( ( sk2 @ sk3 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[9,66]) ).
thf(77,plain,
sk2 @ sk3 @ sk6,
inference(simp,[status(thm)],[76]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A )
| sk1 ),
inference(simp,[status(thm)],[8]) ).
thf(82,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A )
| $false ),
inference(rewrite,[status(thm)],[17,66]) ).
thf(83,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk5 @ A ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [A: $i] :
( ~ ( sk5 @ A )
| ( ( sk2 @ sk3 @ sk6 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[77,83]) ).
thf(85,plain,
~ ( sk5 @ sk6 ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk6 ))]]) ).
thf(11,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ~ ( sk4 @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(38,plain,
! [A: $i] :
( sk1
| ~ ( sk4 @ A )
| ( ( sk2 @ sk3 @ sk6 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,11]) ).
thf(39,plain,
( sk1
| ~ ( sk4 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk6 ))]]) ).
thf(74,plain,
( $false
| ~ ( sk4 @ sk6 ) ),
inference(rewrite,[status(thm)],[39,66]) ).
thf(75,plain,
~ ( sk4 @ sk6 ),
inference(simp,[status(thm)],[74]) ).
thf(89,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[79,85,75]) ).
thf(90,plain,
$false,
inference(simp,[status(thm)],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n025.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 Jun 23 06:52:25 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.00 % [INFO] Parsing done (142ms).
% 1.42/1.01 % [INFO] Running in sequential loop mode.
% 1.83/1.21 % [INFO] nitpick registered as external prover.
% 1.92/1.21 % [INFO] Scanning for conjecture ...
% 2.01/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.33 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.33 % [INFO] Problem is higher-order (TPTP THF).
% 2.31/1.33 % [INFO] Type checking passed.
% 2.31/1.34 % [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 ...
% 4.39/1.93 % [INFO] Killing All external provers ...
% 4.39/1.94 % Time passed: 1401ms (effective reasoning time: 918ms)
% 4.39/1.94 % 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)>
% 4.39/1.94 % Axioms used in derivation (0):
% 4.39/1.94 % No. of inferences in proof: 47
% 4.39/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1401 ms resp. 918 ms w/o parsing
% 4.39/2.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.39/2.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------