TSTP Solution File: ALG203+1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : ALG203+1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 May 20 18:16:10 EDT 2024
% Result : Theorem 15.86s 4.21s
% Output : Refutation 15.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 184 ( 87 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 582 ( 96 ~; 63 |; 27 &; 369 @)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 72 ( 0 ^ 62 !; 10 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(sorti1_type,type,
sorti1: $i > $o ).
thf(sorti2_type,type,
sorti2: $i > $o ).
thf(h_type,type,
h: $i > $i ).
thf(j_type,type,
j: $i > $i ).
thf(op1_type,type,
op1: $i > $i > $i ).
thf(op2_type,type,
op2: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ! [A: $i] :
( ( sorti1 @ A )
=> ( sorti2 @ ( h @ A ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( sorti1 @ ( j @ A ) ) ) )
=> ~ ( ! [A: $i] :
( ( sorti1 @ A )
=> ! [B: $i] :
( ( sorti1 @ B )
=> ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ! [B: $i] :
( ( sorti2 @ B )
=> ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ) )
& ! [A: $i] :
( ( sorti2 @ A )
=> ( ( h @ ( j @ A ) )
= A ) )
& ! [A: $i] :
( ( sorti1 @ A )
=> ( ( j @ ( h @ A ) )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ~ ( sorti1 @ A )
| ~ ( sorti1 @ B )
| ( ( h @ ( op1 @ A @ B ) )
= ( op2 @ ( h @ A ) @ ( h @ B ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ( op2 @ ( h @ A ) @ ( h @ B ) )
= ( h @ ( op1 @ A @ B ) ) )
| ~ ( sorti1 @ A )
| ~ ( sorti1 @ B ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( ( op2 @ ( h @ A ) @ ( h @ B ) )
= ( h @ ( op1 @ A @ B ) ) )
| ~ ( sorti1 @ A )
| ~ ( sorti1 @ B ) ),
inference(simp,[status(thm)],[19]) ).
thf(5,axiom,
( ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(27,plain,
( ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti1 @ A )
& ( ( op1 @ A @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
sorti1 @ sk1,
inference(cnf,[status(esa)],[27]) ).
thf(10,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( sorti2 @ ( h @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(50,plain,
! [A: $i] :
( ( sorti2 @ ( h @ A ) )
| ( ( sorti1 @ sk1 )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[31,10]) ).
thf(51,plain,
sorti2 @ ( h @ sk1 ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk1 ))]]) ).
thf(29,plain,
sorti1 @ sk2,
inference(cnf,[status(esa)],[27]) ).
thf(48,plain,
! [A: $i] :
( ( sorti2 @ ( h @ A ) )
| ( ( sorti1 @ sk2 )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,10]) ).
thf(49,plain,
sorti2 @ ( h @ sk2 ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk2 ))]]) ).
thf(6,axiom,
~ ( ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
!= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(34,plain,
~ ( ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
!= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,plain,
~ ( ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
= A ) )
& ? [A: $i] :
( ( sorti2 @ A )
& ( ( op2 @ A @ A )
!= A ) ) ),
inference(polarity_switch,[status(thm)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ( ( op2 @ A @ A )
!= A )
| ~ ( sorti2 @ B )
| ( ( op2 @ B @ B )
= B ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( op2 @ A @ A )
!= A )
| ( ( op2 @ B @ B )
= B )
| ~ ( sorti2 @ A )
| ~ ( sorti2 @ B ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( op2 @ A @ A )
!= A )
| ( ( op2 @ B @ B )
= B )
| ~ ( sorti2 @ A )
| ( ( sorti2 @ ( h @ sk2 ) )
!= ( sorti2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[49,37]) ).
thf(57,plain,
! [A: $i] :
( ( ( op2 @ A @ A )
!= A )
| ( ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) )
= ( h @ sk2 ) )
| ~ ( sorti2 @ A ) ),
inference(pattern_uni,[status(thm)],[56:[bind(A,$thf( A )),bind(B,$thf( h @ sk2 ))]]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ~ ( sorti2 @ B )
| ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) )
| ~ ( sorti2 @ A )
| ~ ( sorti2 @ B ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( ( j @ ( op2 @ A @ B ) )
= ( op1 @ ( j @ A ) @ ( j @ B ) ) )
| ~ ( sorti2 @ A )
| ~ ( sorti2 @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(28,plain,
( ( op1 @ sk2 @ sk2 )
!= sk2 ),
inference(cnf,[status(esa)],[27]) ).
thf(32,plain,
( ( op1 @ sk2 @ sk2 )
!= sk2 ),
inference(lifteq,[status(thm)],[28]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ~ ( sorti2 @ B )
| ( ( j @ ( op2 @ A @ B ) )
!= sk2 )
| ( ( op1 @ ( j @ A ) @ ( j @ B ) )
!= ( op1 @ sk2 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[15,32]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ~ ( sorti2 @ B )
| ( ( j @ ( op2 @ A @ B ) )
!= sk2 )
| ( ( j @ A )
!= sk2 )
| ( ( j @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[72]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ( ( j @ ( op2 @ A @ B ) )
!= sk2 )
| ( ( j @ A )
!= sk2 )
| ( ( j @ B )
!= sk2 )
| ( ( sorti2 @ ( h @ sk2 ) )
!= ( sorti2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[49,87]) ).
thf(143,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( ( j @ ( op2 @ A @ ( h @ sk2 ) ) )
!= sk2 )
| ( ( j @ A )
!= sk2 )
| ( ( j @ ( h @ sk2 ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( A )),bind(B,$thf( h @ sk2 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( ( j @ ( op2 @ A @ ( h @ sk2 ) ) )
!= sk2 )
| ( ( j @ A )
!= sk2 )
| ( ( j @ ( h @ sk2 ) )
!= sk2 )
| ( ( sorti2 @ ( h @ sk2 ) )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,143]) ).
thf(176,plain,
( ( ( j @ ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) ) )
!= sk2 )
| ( ( j @ ( h @ sk2 ) )
!= sk2 )
| ( ( j @ ( h @ sk2 ) )
!= sk2 ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( h @ sk2 ))]]) ).
thf(193,plain,
( ( ( j @ ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) ) )
!= sk2 )
| ( ( j @ ( h @ sk2 ) )
!= sk2 ) ),
inference(simp,[status(thm)],[176]) ).
thf(388,plain,
( ( ( j @ ( h @ sk2 ) )
!= sk2 )
| ( ( j @ ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) ) )
!= ( j @ ( h @ sk2 ) ) )
| ( sk2 != sk2 ) ),
inference(eqfactor_ordered,[status(thm)],[193]) ).
thf(392,plain,
( ( ( j @ ( h @ sk2 ) )
!= sk2 )
| ( ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) )
!= ( h @ sk2 ) ) ),
inference(simp,[status(thm)],[388]) ).
thf(8,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( ( j @ ( h @ A ) )
= A ) ),
inference(cnf,[status(esa)],[7]) ).
thf(21,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ~ ( sorti1 @ A ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ~ ( sorti1 @ A ) ),
inference(simp,[status(thm)],[21]) ).
thf(649,plain,
! [A: $i] :
( ( ( j @ ( h @ A ) )
= A )
| ( ( sorti1 @ sk2 )
!= ( sorti1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[29,22]) ).
thf(650,plain,
( ( j @ ( h @ sk2 ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[649:[bind(A,$thf( sk2 ))]]) ).
thf(696,plain,
( ( sk2 != sk2 )
| ( ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) )
!= ( h @ sk2 ) ) ),
inference(rewrite,[status(thm)],[392,650]) ).
thf(697,plain,
( ( op2 @ ( h @ sk2 ) @ ( h @ sk2 ) )
!= ( h @ sk2 ) ),
inference(simp,[status(thm)],[696]) ).
thf(1335,plain,
! [A: $i] :
( ( ( op2 @ A @ A )
!= A )
| ~ ( sorti2 @ A ) ),
inference(simplifyReflect,[status(thm)],[57,697]) ).
thf(1344,plain,
! [A: $i] :
( ( ( op2 @ A @ A )
!= A )
| ( ( sorti2 @ ( h @ sk1 ) )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[51,1335]) ).
thf(1345,plain,
( ( op2 @ ( h @ sk1 ) @ ( h @ sk1 ) )
!= ( h @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1344:[bind(A,$thf( h @ sk1 ))]]) ).
thf(1372,plain,
! [B: $i,A: $i] :
( ~ ( sorti1 @ A )
| ~ ( sorti1 @ B )
| ( ( h @ ( op1 @ A @ B ) )
!= ( h @ sk1 ) )
| ( ( op2 @ ( h @ A ) @ ( h @ B ) )
!= ( op2 @ ( h @ sk1 ) @ ( h @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,1345]) ).
thf(1373,plain,
( ~ ( sorti1 @ sk1 )
| ~ ( sorti1 @ sk1 )
| ( ( h @ ( op1 @ sk1 @ sk1 ) )
!= ( h @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1372:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1381,plain,
( ~ ( sorti1 @ sk1 )
| ( ( h @ ( op1 @ sk1 @ sk1 ) )
!= ( h @ sk1 ) ) ),
inference(simp,[status(thm)],[1373]) ).
thf(30,plain,
( ( op1 @ sk1 @ sk1 )
= sk1 ),
inference(cnf,[status(esa)],[27]) ).
thf(33,plain,
( ( op1 @ sk1 @ sk1 )
= sk1 ),
inference(lifteq,[status(thm)],[30]) ).
thf(1383,plain,
( ~ $true
| ( ( h @ sk1 )
!= ( h @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1381,33,31]) ).
thf(1384,plain,
$false,
inference(simp,[status(thm)],[1383]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG203+1 : TPTP v8.2.0. Released v2.7.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n019.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 : Sat May 18 23:38:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.98/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.12 % [INFO] Parsing done (166ms).
% 1.27/1.13 % [INFO] Running in sequential loop mode.
% 1.84/1.49 % [INFO] nitpick registered as external prover.
% 1.92/1.50 % [INFO] Scanning for conjecture ...
% 2.02/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.22/1.65 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.22/1.66 % [INFO] Problem is first-order (TPTP FOF).
% 2.22/1.67 % [INFO] Type checking passed.
% 2.22/1.67 % [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 ...
% 15.86/4.20 % [INFO] Killing All external provers ...
% 15.86/4.21 % Time passed: 3725ms (effective reasoning time: 3066ms)
% 15.86/4.21 % 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)>
% 15.86/4.21 % Axioms used in derivation (2): ax3, ax4
% 15.86/4.21 % No. of inferences in proof: 53
% 15.86/4.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3725 ms resp. 3066 ms w/o parsing
% 15.93/4.32 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.93/4.32 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------