TSTP Solution File: SYO048^1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 08:59:06 EDT 2024
% Result : Theorem 4.39s 2.14s
% Output : Refutation 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 24
% Syntax : Number of formulae : 75 ( 12 unt; 18 typ; 5 def)
% Number of atoms : 166 ( 14 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 411 ( 103 ~; 91 |; 0 &; 217 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 11 con; 0-3 aty)
% Number of variables : 57 ( 13 ^ 44 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_def,definition,
( mand
= ( ^ [A: $i > $o,B: $i > $o] : ( mnot @ ( mor @ ( mnot @ A ) @ ( mnot @ B ) ) ) ) ) ).
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(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(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 ).
thf(sk8_type,type,
sk8: $i > $i > $o ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i > $o ).
thf(sk11_type,type,
sk11: $i > $o ).
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 @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ 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 @ ( mbox @ A @ ( mand @ B @ C ) ) @ ( mand @ ( mbox @ A @ B ) @ ( mbox @ 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(5,plain,
( ( sk2 @ sk3 @ sk6 )
| ( sk2 @ sk3 @ sk7 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
( ~ sk1
| ( sk8 @ sk9 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk8 @ sk9 @ A )
| ( sk11 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk8 @ sk9 @ A )
| ( sk11 @ A ) ),
inference(simp,[status(thm)],[14]) ).
thf(19,plain,
! [A: $i] :
( ~ sk1
| ( sk11 @ A )
| ( ( sk8 @ sk9 @ sk12 )
!= ( sk8 @ sk9 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,16]) ).
thf(20,plain,
( ~ sk1
| ( sk11 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[19:[bind(A,$thf( sk12 ))]]) ).
thf(10,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk8 @ sk9 @ A )
| ( sk10 @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(15,plain,
! [A: $i] :
( ~ sk1
| ~ ( sk8 @ sk9 @ A )
| ( sk10 @ A ) ),
inference(simp,[status(thm)],[10]) ).
thf(17,plain,
! [A: $i] :
( ~ sk1
| ( sk10 @ A )
| ( ( sk8 @ sk9 @ sk12 )
!= ( sk8 @ sk9 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,15]) ).
thf(18,plain,
( ~ sk1
| ( sk10 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[17:[bind(A,$thf( sk12 ))]]) ).
thf(11,plain,
( ~ sk1
| ~ ( sk10 @ sk12 )
| ~ ( sk11 @ sk12 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
( ~ sk1
| ~ ( sk11 @ sk12 )
| ( ( sk10 @ sk12 )
!= ( sk10 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[18,11]) ).
thf(26,plain,
( ~ sk1
| ~ ( sk11 @ sk12 ) ),
inference(pattern_uni,[status(thm)],[25:[]]) ).
thf(33,plain,
( ~ sk1
| ( ( sk11 @ sk12 )
!= ( sk11 @ sk12 ) ) ),
inference(paramod_ordered,[status(thm)],[20,26]) ).
thf(34,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[33:[]]) ).
thf(35,plain,
( ( sk2 @ sk3 @ sk6 )
| ( sk2 @ sk3 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[5,34]) ).
thf(36,plain,
( ( sk2 @ sk3 @ sk6 )
| ( sk2 @ sk3 @ sk7 ) ),
inference(simp,[status(thm)],[35]) ).
thf(12,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk5 @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(55,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk5 @ A )
| $false ),
inference(rewrite,[status(thm)],[12,34]) ).
thf(56,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk5 @ A ) ),
inference(simp,[status(thm)],[55]) ).
thf(85,plain,
! [A: $i] :
( ( sk2 @ sk3 @ sk6 )
| ( sk5 @ A )
| ( ( sk2 @ sk3 @ sk7 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[36,56]) ).
thf(86,plain,
( ( sk2 @ sk3 @ sk6 )
| ( sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( sk7 ))]]) ).
thf(6,plain,
( ( sk2 @ sk3 @ sk6 )
| ~ ( sk5 @ sk7 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(37,plain,
( ( sk2 @ sk3 @ sk6 )
| ~ ( sk5 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[6,34]) ).
thf(38,plain,
( ( sk2 @ sk3 @ sk6 )
| ~ ( sk5 @ sk7 ) ),
inference(simp,[status(thm)],[37]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk4 @ A )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(41,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk4 @ A )
| $false ),
inference(rewrite,[status(thm)],[8,34]) ).
thf(42,plain,
! [A: $i] :
( ~ ( sk2 @ sk3 @ A )
| ( sk4 @ A ) ),
inference(simp,[status(thm)],[41]) ).
thf(44,plain,
! [A: $i] :
( ~ ( sk5 @ sk7 )
| ( sk4 @ A )
| ( ( sk2 @ sk3 @ sk6 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[38,42]) ).
thf(45,plain,
( ~ ( sk5 @ sk7 )
| ( sk4 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( sk6 ))]]) ).
thf(13,plain,
( ~ ( sk4 @ sk6 )
| ( sk2 @ sk3 @ sk7 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(96,plain,
( ~ ( sk4 @ sk6 )
| ( sk2 @ sk3 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[13,34]) ).
thf(97,plain,
( ~ ( sk4 @ sk6 )
| ( sk2 @ sk3 @ sk7 ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [A: $i] :
( ~ ( sk4 @ sk6 )
| ( sk5 @ A )
| ( ( sk2 @ sk3 @ sk7 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[97,56]) ).
thf(99,plain,
( ~ ( sk4 @ sk6 )
| ( sk5 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( sk7 ))]]) ).
thf(7,plain,
( ~ ( sk4 @ sk6 )
| ~ ( sk5 @ sk7 )
| sk1 ),
inference(cnf,[status(esa)],[4]) ).
thf(39,plain,
( ~ ( sk4 @ sk6 )
| ~ ( sk5 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[7,34]) ).
thf(40,plain,
( ~ ( sk4 @ sk6 )
| ~ ( sk5 @ sk7 ) ),
inference(simp,[status(thm)],[39]) ).
thf(112,plain,
( ~ ( sk4 @ sk6 )
| ( ( sk5 @ sk7 )
!= ( sk5 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[99,40]) ).
thf(113,plain,
~ ( sk4 @ sk6 ),
inference(pattern_uni,[status(thm)],[112:[]]) ).
thf(126,plain,
( ~ ( sk5 @ sk7 )
| $false ),
inference(rewrite,[status(thm)],[45,113]) ).
thf(127,plain,
~ ( sk5 @ sk7 ),
inference(simp,[status(thm)],[126]) ).
thf(155,plain,
( ( sk2 @ sk3 @ sk6 )
| $false ),
inference(rewrite,[status(thm)],[86,127]) ).
thf(156,plain,
sk2 @ sk3 @ sk6,
inference(simp,[status(thm)],[155]) ).
thf(159,plain,
! [A: $i] :
( ( sk4 @ A )
| ( ( sk2 @ sk3 @ sk6 )
!= ( sk2 @ sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[156,42]) ).
thf(160,plain,
sk4 @ sk6,
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( sk6 ))]]) ).
thf(166,plain,
$false,
inference(rewrite,[status(thm)],[160,113]) ).
thf(167,plain,
$false,
inference(simp,[status(thm)],[166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO048^1 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n012.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 20 08:40:54 EDT 2024
% 0.17/0.38 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.04 % [INFO] Parsing done (148ms).
% 1.28/1.05 % [INFO] Running in sequential loop mode.
% 1.98/1.28 % [INFO] nitpick registered as external prover.
% 1.98/1.28 % [INFO] Scanning for conjecture ...
% 2.25/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.43/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.43/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.43/1.43 % [INFO] Type checking passed.
% 2.43/1.43 % [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 ...
% 4.39/2.13 % [INFO] Killing All external provers ...
% 4.39/2.13 % Time passed: 1589ms (effective reasoning time: 1080ms)
% 4.39/2.13 % 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)>
% 4.39/2.14 % Axioms used in derivation (0):
% 4.39/2.14 % No. of inferences in proof: 52
% 4.39/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1589 ms resp. 1080 ms w/o parsing
% 4.57/2.19 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.57/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------