TSTP Solution File: LCL725^1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n005.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 00:11:01 EDT 2024
% Result : Theorem 24.53s 5.34s
% Output : Refutation 24.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of formulae : 92 ( 19 unt; 18 typ; 7 def)
% Number of atoms : 241 ( 18 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 416 ( 78 ~; 90 |; 8 &; 236 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 13 con; 0-3 aty)
% Number of variables : 63 ( 7 ^ 56 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: $i > $o] : ( mor @ ( mnot @ A ) ) ) ) ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mreflexive_def,definition,
( mreflexive
= ( ^ [A: $i > $i > $o] :
! [B: $i] : ( A @ B @ B ) ) ) ).
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(mdia_s5_type,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(mdia_s5_def,definition,
( mdia_s5
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ A ) ) ) ) ) ).
thf(phi_type,type,
phi: $i > $o ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(1,conjecture,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ( ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( phi @ B ) )
| ( phi @ A ) )
& ! [A: $i] :
( ~ ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ( phi @ B ) )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ( phi @ C ) ) ) )
& ! [A: $i] :
( ~ ( phi @ A )
| ! [B: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ! [C: $i] :
( ~ ( rel_s5 @ B @ C )
| ~ ( phi @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
( sk1
| ( rel_s5 @ sk5 @ sk6 )
| ~ sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(3,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
thf(18,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [A: $i] : ( rel_s5 @ A @ A ),
inference(cnf,[status(esa)],[18]) ).
thf(12,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk2 @ A )
| ( phi @ A )
| ~ sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( phi @ B )
| ~ sk1
| ( ( rel_s5 @ A @ A )
!= ( rel_s5 @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[19,12]) ).
thf(31,plain,
( ( phi @ sk2 )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(9,plain,
( ~ ( phi @ sk2 )
| ~ sk1 ),
inference(cnf,[status(esa)],[6]) ).
thf(40,plain,
( ~ sk1
| ( ( phi @ sk2 )
!= ( phi @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[31,9]) ).
thf(41,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[40:[]]) ).
thf(187,plain,
( $false
| ( rel_s5 @ sk5 @ sk6 )
| ~ sk3 ),
inference(rewrite,[status(thm)],[11,41]) ).
thf(188,plain,
( ( rel_s5 @ sk5 @ sk6 )
| ~ sk3 ),
inference(simp,[status(thm)],[187]) ).
thf(15,plain,
( sk1
| sk3
| ( phi @ sk7 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(44,plain,
( $false
| sk3
| ( phi @ sk7 ) ),
inference(rewrite,[status(thm)],[15,41]) ).
thf(45,plain,
( sk3
| ( phi @ sk7 ) ),
inference(simp,[status(thm)],[44]) ).
thf(14,plain,
( sk1
| sk3
| ( rel_s5 @ sk7 @ sk8 ) ),
inference(cnf,[status(esa)],[6]) ).
thf(153,plain,
( $false
| sk3
| ( rel_s5 @ sk7 @ sk8 ) ),
inference(rewrite,[status(thm)],[14,41]) ).
thf(154,plain,
( sk3
| ( rel_s5 @ sk7 @ sk8 ) ),
inference(simp,[status(thm)],[153]) ).
thf(5,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( rel_s5 @ A @ B )
=> ( rel_s5 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ B @ A ) ),
inference(cnf,[status(esa)],[22]) ).
thf(165,plain,
! [B: $i,A: $i] :
( sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk7 @ sk8 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[154,23]) ).
thf(166,plain,
( sk3
| ( rel_s5 @ sk8 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( sk7 )),bind(B,$thf( sk8 ))]]) ).
thf(13,plain,
! [A: $i] :
( sk1
| sk3
| ~ ( rel_s5 @ sk8 @ A )
| ~ ( phi @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(16,plain,
! [A: $i] :
( sk1
| sk3
| ~ ( rel_s5 @ sk8 @ A )
| ~ ( phi @ A ) ),
inference(simp,[status(thm)],[13]) ).
thf(205,plain,
! [A: $i] :
( $false
| sk3
| ~ ( rel_s5 @ sk8 @ A )
| ~ ( phi @ A ) ),
inference(rewrite,[status(thm)],[16,41]) ).
thf(206,plain,
! [A: $i] :
( sk3
| ~ ( rel_s5 @ sk8 @ A )
| ~ ( phi @ A ) ),
inference(simp,[status(thm)],[205]) ).
thf(218,plain,
! [A: $i] :
( sk3
| ~ ( phi @ A )
| ( ( rel_s5 @ sk8 @ sk7 )
!= ( rel_s5 @ sk8 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[166,206]) ).
thf(219,plain,
( sk3
| ~ ( phi @ sk7 ) ),
inference(pattern_uni,[status(thm)],[218:[bind(A,$thf( sk7 ))]]) ).
thf(228,plain,
( sk3
| ( ( phi @ sk7 )
!= ( phi @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[45,219]) ).
thf(229,plain,
sk3,
inference(pattern_uni,[status(thm)],[228:[]]) ).
thf(230,plain,
( ( rel_s5 @ sk5 @ sk6 )
| ~ $true ),
inference(rewrite,[status(thm)],[188,229]) ).
thf(231,plain,
rel_s5 @ sk5 @ sk6,
inference(simp,[status(thm)],[230]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk5 @ sk6 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[231,23]) ).
thf(675,plain,
rel_s5 @ sk6 @ sk5,
inference(pattern_uni,[status(thm)],[674:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(8,plain,
( sk1
| ( rel_s5 @ sk4 @ sk5 )
| ~ sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(46,plain,
( $false
| ( rel_s5 @ sk4 @ sk5 )
| ~ sk3 ),
inference(rewrite,[status(thm)],[8,41]) ).
thf(47,plain,
( ( rel_s5 @ sk4 @ sk5 )
| ~ sk3 ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ sk3
| ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk4 @ sk5 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47,23]) ).
thf(49,plain,
( ~ sk3
| ( rel_s5 @ sk5 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk4 )),bind(B,$thf( sk5 ))]]) ).
thf(4,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(20,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(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( rel_s5 @ A @ B )
| ~ ( rel_s5 @ B @ C )
| ( rel_s5 @ A @ C ) ),
inference(cnf,[status(esa)],[20]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk3
| ~ ( rel_s5 @ A @ B )
| ( rel_s5 @ A @ C )
| ( ( rel_s5 @ sk5 @ sk4 )
!= ( rel_s5 @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[49,21]) ).
thf(61,plain,
! [A: $i] :
( ~ sk3
| ~ ( rel_s5 @ A @ sk5 )
| ( rel_s5 @ A @ sk4 ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( sk5 )),bind(C,$thf( sk4 ))]]) ).
thf(1955,plain,
! [A: $i] :
( ~ $true
| ~ ( rel_s5 @ A @ sk5 )
| ( rel_s5 @ A @ sk4 ) ),
inference(rewrite,[status(thm)],[61,229]) ).
thf(1956,plain,
! [A: $i] :
( ~ ( rel_s5 @ A @ sk5 )
| ( rel_s5 @ A @ sk4 ) ),
inference(simp,[status(thm)],[1955]) ).
thf(1958,plain,
! [A: $i] :
( ( rel_s5 @ A @ sk4 )
| ( ( rel_s5 @ sk6 @ sk5 )
!= ( rel_s5 @ A @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[675,1956]) ).
thf(1959,plain,
rel_s5 @ sk6 @ sk4,
inference(pattern_uni,[status(thm)],[1958:[bind(A,$thf( sk6 ))]]) ).
thf(2060,plain,
! [B: $i,A: $i] :
( ( rel_s5 @ B @ A )
| ( ( rel_s5 @ sk6 @ sk4 )
!= ( rel_s5 @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1959,23]) ).
thf(2061,plain,
rel_s5 @ sk4 @ sk6,
inference(pattern_uni,[status(thm)],[2060:[bind(A,$thf( sk6 )),bind(B,$thf( sk4 ))]]) ).
thf(7,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ sk4 @ A )
| ( phi @ A )
| ~ sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(17,plain,
! [A: $i] :
( sk1
| ~ ( rel_s5 @ sk4 @ A )
| ( phi @ A )
| ~ sk3 ),
inference(simp,[status(thm)],[7]) ).
thf(777,plain,
! [A: $i] :
( $false
| ~ ( rel_s5 @ sk4 @ A )
| ( phi @ A )
| ~ $true ),
inference(rewrite,[status(thm)],[17,229,41]) ).
thf(778,plain,
! [A: $i] :
( ~ ( rel_s5 @ sk4 @ A )
| ( phi @ A ) ),
inference(simp,[status(thm)],[777]) ).
thf(2161,plain,
! [A: $i] :
( ( phi @ A )
| ( ( rel_s5 @ sk4 @ sk6 )
!= ( rel_s5 @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2061,778]) ).
thf(2162,plain,
phi @ sk6,
inference(pattern_uni,[status(thm)],[2161:[bind(A,$thf( sk6 ))]]) ).
thf(10,plain,
( sk1
| ~ ( phi @ sk6 )
| ~ sk3 ),
inference(cnf,[status(esa)],[6]) ).
thf(42,plain,
( $false
| ~ ( phi @ sk6 )
| ~ sk3 ),
inference(rewrite,[status(thm)],[10,41]) ).
thf(43,plain,
( ~ ( phi @ sk6 )
| ~ sk3 ),
inference(simp,[status(thm)],[42]) ).
thf(234,plain,
( ~ ( phi @ sk6 )
| ~ $true ),
inference(rewrite,[status(thm)],[43,229]) ).
thf(235,plain,
~ ( phi @ sk6 ),
inference(simp,[status(thm)],[234]) ).
thf(2216,plain,
$false,
inference(rewrite,[status(thm)],[2162,235]) ).
thf(2217,plain,
$false,
inference(simp,[status(thm)],[2216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL725^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n005.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 : Mon May 20 03:03:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.16 % [INFO] Parsing done (224ms).
% 1.25/1.18 % [INFO] Running in sequential loop mode.
% 2.06/1.52 % [INFO] nitpick registered as external prover.
% 2.06/1.53 % [INFO] Scanning for conjecture ...
% 2.51/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.51/1.73 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.51/1.73 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.73 % [INFO] Type checking passed.
% 2.51/1.74 % [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 ...
% 24.37/5.27 % [INFO] Killing All external provers ...
% 24.48/5.34 % Time passed: 4796ms (effective reasoning time: 4091ms)
% 24.48/5.34 % 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)>
% 24.48/5.34 % Axioms used in derivation (3): a1, a3, a2
% 24.48/5.34 % No. of inferences in proof: 67
% 24.53/5.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4796 ms resp. 4091 ms w/o parsing
% 24.75/5.42 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.75/5.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------