TSTP Solution File: SYO448^1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SYO448^1 : TPTP v8.2.0. Released v4.0.0.
% 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 20:55:27 EDT 2024
% Result : Theorem 136.85s 24.86s
% Output : Refutation 136.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 17 unt; 0 typ; 6 def)
% Number of atoms : 117 ( 13 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 218 ( 28 ~; 27 |; 2 &; 157 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 48 ( 8 ^ 40 !; 0 ?; 48 :)
% 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(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(msymmetric_def,definition,
( msymmetric
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ( A @ C @ B ) ) ) ) ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mtransitive_def,definition,
( mtransitive
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid_def,definition,
( mvalid
= ( '!' @ $i ) ) ).
thf(rel_s5_type,type,
rel_s5: $i > $i > $o ).
thf(mbox_s5_type,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(mbox_s5_def,definition,
( mbox_s5
= ( ^ [A: $i > $o,B: $i] :
! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( A @ C ) ) ) ) ).
thf(p_type,type,
p: $i > $o ).
thf(q_type,type,
q: $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(2,negated_conjecture,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( p @ C ) )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( q @ C ) )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( p @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
rel_s5 @ sk1 @ sk2,
inference(cnf,[status(esa)],[6]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[20]) ).
thf(727,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk1 @ sk2 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,21]) ).
thf(728,plain,
rel_s5 @ sk2 @ sk1,
inference(pattern_uni,[status(thm)],[727:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(7,plain,
rel_s5 @ sk1 @ sk4,
inference(cnf,[status(esa)],[6]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( ( rel_s5 @ A @ B )
& ( rel_s5 @ B @ C ) )
=> ( rel_s5 @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk1 @ sk4 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7,19]) ).
thf(25,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk1 )
| ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk4 ))]]) ).
thf(2167,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk4 )
| ( ( rel_s5 @ sk2 @ sk1 )
!= ( rel_s5 @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[728,25]) ).
thf(2168,plain,
rel_s5 @ sk2 @ sk4,
inference(pattern_uni,[status(thm)],[2167:[bind(A,$thf( sk2 ))]]) ).
thf(2489,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk2 @ sk4 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2168,21]) ).
thf(2490,plain,
rel_s5 @ sk4 @ sk2,
inference(pattern_uni,[status(thm)],[2489:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(8,plain,
rel_s5 @ sk2 @ sk3,
inference(cnf,[status(esa)],[6]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk2 @ sk3 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8,19]) ).
thf(29,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk2 )
| ( rel_s5 @ A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[28:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(16833,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk3 )
| ( ( rel_s5 @ sk4 @ sk2 )
!= ( rel_s5 @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2490,29]) ).
thf(16834,plain,
rel_s5 @ sk4 @ sk3,
inference(pattern_uni,[status(thm)],[16833:[bind(A,$thf( sk4 ))]]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( q @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(15,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( q @ A ) ),
inference(simp,[status(thm)],[12]) ).
thf(17373,plain,
! [A: $i] :
( ( q @ A )
| ( ( rel_s5 @ sk4 @ sk3 )
!= ( rel_s5 @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[16834,15]) ).
thf(17374,plain,
q @ sk3,
inference(pattern_uni,[status(thm)],[17373:[bind(A,$thf( sk3 ))]]) ).
thf(11,plain,
~ ( q @ sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(17514,plain,
$false,
inference(rewrite,[status(thm)],[17374,11]) ).
thf(17515,plain,
$false,
inference(simp,[status(thm)],[17514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO448^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % 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 : Sun Jun 23 10:53:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.97/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/1.08 % [INFO] Parsing done (162ms).
% 1.56/1.09 % [INFO] Running in sequential loop mode.
% 1.93/1.30 % [INFO] nitpick registered as external prover.
% 1.93/1.31 % [INFO] Scanning for conjecture ...
% 2.25/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.25/1.44 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.25/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.25/1.44 % [INFO] Type checking passed.
% 2.25/1.44 % [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 ...
% 136.85/24.85 % [INFO] Killing All external provers ...
% 136.85/24.85 % Time passed: 24311ms (effective reasoning time: 23755ms)
% 136.85/24.85 % 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)>
% 136.85/24.86 % Axioms used in derivation (2): a3, a2
% 136.85/24.86 % No. of inferences in proof: 31
% 136.85/24.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24311 ms resp. 23755 ms w/o parsing
% 136.92/24.95 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 136.92/24.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------