TSTP Solution File: SWV425^2 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWV425^2 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.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 05:45:36 EDT 2024
% Result : Theorem 10.15s 3.01s
% Output : Refutation 10.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 97 ( 29 unt; 21 typ; 8 def)
% Number of atoms : 234 ( 36 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 474 ( 75 ~; 64 |; 0 &; 326 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 85 ( 15 ^ 70 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
thf(prop_a_type,type,
prop_a: $i > $o ).
thf(prop_b_type,type,
prop_b: $i > $o ).
thf(prop_c_type,type,
prop_c: $i > $o ).
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(rel_type,type,
rel: $i > $i > $o ).
thf(icl_atom_type,type,
icl_atom: ( $i > $o ) > $i > $o ).
thf(icl_atom_def,definition,
( icl_atom
= ( mbox @ rel ) ) ).
thf(icl_princ_type,type,
icl_princ: ( $i > $o ) > $i > $o ).
thf(icl_princ_def,definition,
( icl_princ
= ( ^ [A: $i > $o] : A ) ) ).
thf(icl_impl_type,type,
icl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(icl_impl_def,definition,
( icl_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mimpl @ A @ B ) ) ) ) ).
thf(icl_says_type,type,
icl_says: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(icl_says_def,definition,
( icl_says
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ rel @ ( mor @ A @ B ) ) ) ) ).
thf(iclval_type,type,
iclval: ( $i > $o ) > $o ).
thf(iclval_def,definition,
iclval = mvalid ).
thf(s_type,type,
s: $i > $o ).
thf(a_type,type,
a: $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(sk5_type,type,
sk5: $i > ( $i > $o ) > $i ).
thf(sk6_type,type,
sk6: $i > ( $i > $o ) > $i ).
thf(3,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom) ).
thf(12,plain,
! [A: $i > $o,B: $i] :
( ~ ! [C: $i] :
( ( rel @ B @ C )
=> ( A @ C ) )
| ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [B: $i,A: $i > $o] :
( ( rel @ B @ ( sk5 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[12]) ).
thf(1,conjecture,
iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unit) ).
thf(2,negated_conjecture,
~ ( iclval @ ( icl_impl @ ( icl_atom @ s ) @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i,B: $i] :
( ( rel @ A @ B )
=> ( ~ ! [C: $i] :
( ( rel @ B @ C )
=> ( s @ C ) )
| ! [C: $i] :
( ( rel @ B @ C )
=> ( ( a @ C )
| ! [D: $i] :
( ( rel @ C @ D )
=> ( s @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: $i] :
( ~ ( rel @ sk2 @ A )
| ( s @ A ) ),
inference(cnf,[status(esa)],[5]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i > $o] :
( ( A @ B )
| ( s @ C )
| ( ( rel @ B @ ( sk5 @ B @ A ) )
!= ( rel @ sk2 @ C ) ) ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(144,plain,
! [A: $i > $o] :
( ( A @ sk2 )
| ( s @ ( sk5 @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( E )),bind(B,$thf( sk2 )),bind(C,$thf( sk5 @ sk2 @ E ))]]) ).
thf(177,plain,
! [A: $i > $o] :
( ( A @ sk2 )
| ( s @ ( sk5 @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(468,plain,
( ( prop_c @ sk2 )
| ( s @ ( sk5 @ sk2 @ prop_c ) ) ),
inference(prim_subst,[status(thm)],[177:[bind(A,$thf( prop_c ))]]) ).
thf(10,plain,
rel @ sk2 @ sk3,
inference(cnf,[status(esa)],[5]) ).
thf(14,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk5 @ B @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[12]) ).
thf(115,plain,
! [A: $i] :
( ( s @ A )
| ( ( rel @ sk2 @ sk3 )
!= ( rel @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,8]) ).
thf(116,plain,
s @ sk3,
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( sk3 ))]]) ).
thf(9,plain,
~ ( s @ sk4 ),
inference(cnf,[status(esa)],[5]) ).
thf(812,plain,
( ( prop_c @ sk2 )
| ( ( s @ ( sk5 @ sk2 @ prop_c ) )
!= ( s @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[468,9]) ).
thf(815,plain,
( ( prop_c @ sk2 )
| ( ( sk5 @ sk2 @ prop_c )
!= sk4 ) ),
inference(simp,[status(thm)],[812]) ).
thf(4,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ rel @ A ) @ ( mbox @ rel @ ( mbox @ rel @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_axiom) ).
thf(15,plain,
! [A: $i > $o,B: $i] :
( ~ ! [C: $i] :
( ( rel @ B @ C )
=> ( A @ C ) )
| ! [C: $i] :
( ( rel @ B @ C )
=> ! [D: $i] :
( ( rel @ C @ D )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,plain,
! [D: $i,C: $i,B: $i,A: $i > $o] :
( ~ ( A @ ( sk6 @ B @ A ) )
| ~ ( rel @ B @ C )
| ~ ( rel @ C @ D )
| ( A @ D ) ),
inference(cnf,[status(esa)],[15]) ).
thf(7,plain,
~ ( a @ sk3 ),
inference(cnf,[status(esa)],[5]) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i > $o] :
( ~ ( A @ ( sk6 @ B @ A ) )
| ~ ( rel @ B @ C )
| ~ ( rel @ C @ D )
| ( ( A @ D )
!= ( a @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[17,7]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ A @ B )
| ~ ( rel @ B @ sk3 ) ),
inference(pre_uni,[status(thm)],[32:[bind(A,$thf( a )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk3 ))]]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ A @ B )
| ~ ( rel @ B @ sk3 ) ),
inference(simp,[status(thm)],[65]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ A @ B )
| ( ( rel @ B @ sk3 )
!= ( rel @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[73]) ).
thf(285,plain,
( ~ ( a @ ( sk6 @ sk3 @ a ) )
| ~ ( rel @ sk3 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(476,plain,
( ( prop_b @ sk2 )
| ( s @ ( sk5 @ sk2 @ prop_b ) ) ),
inference(prim_subst,[status(thm)],[177:[bind(A,$thf( prop_b ))]]) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i > $o] :
( ~ ( A @ ( sk6 @ B @ A ) )
| ~ ( rel @ B @ C )
| ( A @ D )
| ( ( rel @ sk2 @ sk3 )
!= ( rel @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,17]) ).
thf(22,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ ( sk6 @ B @ A ) )
| ~ ( rel @ B @ sk2 )
| ( A @ sk3 ) ),
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 )),bind(D,$thf( sk3 ))]]) ).
thf(446,plain,
! [C: $i,B: $i > $o,A: $i > $o] :
( ( A @ sk2 )
| ( B @ C )
| ( ( s @ ( sk5 @ sk2 @ A ) )
!= ( B @ ( sk5 @ C @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[177,14]) ).
thf(489,plain,
( ( s @ sk2 )
| ( s @ sk2 ) ),
inference(pre_uni,[status(thm)],[446:[bind(A,$thf( s )),bind(B,$thf( s )),bind(C,$thf( sk2 ))]]) ).
thf(520,plain,
s @ sk2,
inference(simp,[status(thm)],[489]) ).
thf(128,plain,
( ( s @ sk4 )
!= ( s @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[116,9]) ).
thf(130,plain,
sk4 != sk3,
inference(simp,[status(thm)],[128]) ).
thf(150,plain,
! [A: $i] :
( ( rel @ A
@ ( sk5 @ A
@ ^ [B: $i] : $false ) )
| $false ),
inference(prim_subst,[status(thm)],[13:[bind(A,$thf( ^ [C: $i] : $false ))]]) ).
thf(182,plain,
! [A: $i] :
( rel @ A
@ ( sk5 @ A
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[150]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( s @ B )
| ( ( rel @ A
@ ( sk5 @ A
@ ^ [C: $i] : $false ) )
!= ( rel @ sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[182,8]) ).
thf(231,plain,
( s
@ ( sk5 @ sk2
@ ^ [A: $i] : $false ) ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( sk2 )),bind(B,$thf( sk5 @ sk2 @ ^ [C: $i] : $false ))]]) ).
thf(306,plain,
( ( s
@ ( sk5 @ sk2
@ ^ [A: $i] : $false ) )
!= ( s @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[231,9]) ).
thf(310,plain,
( ( sk5 @ sk2
@ ^ [A: $i] : $false )
!= sk4 ),
inference(simp,[status(thm)],[306]) ).
thf(11,plain,
rel @ sk1 @ sk2,
inference(cnf,[status(esa)],[5]) ).
thf(142,plain,
! [B: $i,A: $i > $o] :
( ( rel @ B @ ( sk5 @ B @ A ) )
| ( ( A @ B )
!= ( a @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[13,7]) ).
thf(168,plain,
rel @ sk3 @ ( sk5 @ sk3 @ a ),
inference(pre_uni,[status(thm)],[142:[bind(A,$thf( a )),bind(B,$thf( sk3 ))]]) ).
thf(133,plain,
! [B: $i,A: $i > $o] :
( ( rel @ B @ ( sk5 @ B @ A ) )
| ( ( A @ B )
!= ( s @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[13,9]) ).
thf(170,plain,
rel @ sk4 @ ( sk5 @ sk4 @ s ),
inference(pre_uni,[status(thm)],[133:[bind(A,$thf( s )),bind(B,$thf( sk4 ))]]) ).
thf(6,plain,
rel @ sk3 @ sk4,
inference(cnf,[status(esa)],[5]) ).
thf(526,plain,
( ( s @ sk4 )
!= ( s @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[520,9]) ).
thf(529,plain,
sk4 != sk2,
inference(simp,[status(thm)],[526]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ B @ sk3 )
| ( ( rel @ sk1 @ sk2 )
!= ( rel @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,73]) ).
thf(265,plain,
( ~ ( a @ ( sk6 @ sk1 @ a ) )
| ~ ( rel @ sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(996,plain,
( ~ ( a @ ( sk6 @ sk1 @ a ) )
| ~ $true ),
inference(rewrite,[status(thm)],[265,10]) ).
thf(997,plain,
~ ( a @ ( sk6 @ sk1 @ a ) ),
inference(simp,[status(thm)],[996]) ).
thf(117,plain,
! [A: $i] :
( ( s @ A )
| ( ( rel @ sk3 @ sk4 )
!= ( rel @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,8]) ).
thf(120,plain,
! [A: $i] :
( ( s @ A )
| ( sk3 != sk2 )
| ( sk4 != A ) ),
inference(simp,[status(thm)],[117]) ).
thf(124,plain,
( ( s @ sk4 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[120]) ).
thf(317,plain,
( $false
| ( sk3 != sk2 ) ),
inference(rewrite,[status(thm)],[124,9]) ).
thf(318,plain,
sk3 != sk2,
inference(simp,[status(thm)],[317]) ).
thf(16,plain,
! [D: $i,C: $i,B: $i,A: $i > $o] :
( ( rel @ B @ ( sk6 @ B @ A ) )
| ~ ( rel @ B @ C )
| ~ ( rel @ C @ D )
| ( A @ D ) ),
inference(cnf,[status(esa)],[15]) ).
thf(465,plain,
( ( prop_a @ sk2 )
| ( s @ ( sk5 @ sk2 @ prop_a ) ) ),
inference(prim_subst,[status(thm)],[177:[bind(A,$thf( prop_a ))]]) ).
thf(805,plain,
( ( prop_a @ sk2 )
| ( ( s @ ( sk5 @ sk2 @ prop_a ) )
!= ( s @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[465,9]) ).
thf(808,plain,
( ( prop_a @ sk2 )
| ( ( sk5 @ sk2 @ prop_a )
!= sk4 ) ),
inference(simp,[status(thm)],[805]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ B @ sk3 )
| ( ( rel @ sk3 @ sk4 )
!= ( rel @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[6,73]) ).
thf(250,plain,
( ~ ( a @ ( sk6 @ sk3 @ a ) )
| ~ ( rel @ sk4 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ~ ( a @ ( sk6 @ A @ a ) )
| ~ ( rel @ B @ sk3 )
| ( ( rel @ sk2 @ sk3 )
!= ( rel @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,73]) ).
thf(246,plain,
( ~ ( a @ ( sk6 @ sk2 @ a ) )
| ~ ( rel @ sk3 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(478,plain,
( ( a @ sk2 )
| ( s @ ( sk5 @ sk2 @ a ) ) ),
inference(prim_subst,[status(thm)],[177:[bind(A,$thf( a ))]]) ).
thf(1241,plain,
$false,
inference(e,[status(thm)],[468,10,14,116,815,285,9,476,73,17,22,12,520,130,310,11,168,15,170,5,6,529,997,13,7,318,16,808,177,182,250,465,231,8,246,478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV425^2 : TPTP v8.2.0. Released v3.6.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n011.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 08:21:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 1.03/0.91 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.31/1.08 % [INFO] Parsing done (166ms).
% 1.55/1.09 % [INFO] Running in sequential loop mode.
% 1.79/1.30 % [INFO] eprover registered as external prover.
% 1.79/1.30 % [INFO] cvc4 registered as external prover.
% 1.79/1.30 % [INFO] Scanning for conjecture ...
% 2.02/1.39 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.20/1.41 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.20/1.41 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.41 % [INFO] Type checking passed.
% 2.20/1.41 % [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 ...
% 10.15/3.00 % External prover 'e' found a proof!
% 10.15/3.00 % [INFO] Killing All external provers ...
% 10.15/3.01 % Time passed: 2476ms (effective reasoning time: 1913ms)
% 10.15/3.01 % 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)>
% 10.15/3.01 % Axioms used in derivation (2): refl_axiom, trans_axiom
% 10.15/3.01 % No. of inferences in proof: 68
% 10.15/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2476 ms resp. 1913 ms w/o parsing
% 10.15/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.15/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------