TSTP Solution File: ALG201+1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : ALG201+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 7 10:25:21 EDT 2024
% Result : Theorem 4.44s 2.32s
% Output : Refutation 4.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 5 unt; 7 typ; 0 def)
% Number of atoms : 98 ( 36 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 318 ( 46 ~; 22 |; 12 &; 206 @)
% ( 0 <=>; 32 =>; 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 : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 ^ 46 !; 0 ?; 46 :)
% 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(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(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(6,axiom,
~ ! [A: $i] :
( ( sorti2 @ A )
=> ( ( op2 @ A @ A )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(30,plain,
~ ! [A: $i] :
( ( sorti2 @ A )
=> ( ( op2 @ A @ A )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31,plain,
~ ! [A: $i] :
( ( sorti2 @ A )
=> ( ( op2 @ A @ A )
!= A ) ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(33,plain,
sorti2 @ sk1,
inference(cnf,[status(esa)],[31]) ).
thf(13,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( sorti1 @ ( j @ A ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(16,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( sorti1 @ ( j @ A ) ) ),
inference(simp,[status(thm)],[13]) ).
thf(5,axiom,
! [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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
! [A: $i] :
( ~ ( sorti1 @ A )
| ( ( op1 @ A @ A )
!= A ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( ( op1 @ A @ A )
!= A )
| ~ ( sorti1 @ A ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ( ( op1 @ B @ B )
!= B )
| ( ( sorti1 @ ( j @ A ) )
!= ( sorti1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,29]) ).
thf(44,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( ( op1 @ ( j @ A ) @ ( j @ A ) )
!= ( j @ A ) ) ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( C )),bind(B,$thf( j @ C ))]]) ).
thf(45,plain,
! [A: $i] :
( ~ ( sorti2 @ A )
| ( ( op1 @ ( j @ A ) @ ( j @ A ) )
!= ( j @ A ) ) ),
inference(simp,[status(thm)],[44]) ).
thf(48,plain,
! [A: $i] :
( ( ( op1 @ ( j @ A ) @ ( j @ A ) )
!= ( j @ A ) )
| ( ( sorti2 @ sk1 )
!= ( sorti2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,45]) ).
thf(49,plain,
( ( op1 @ ( j @ sk1 ) @ ( j @ sk1 ) )
!= ( j @ sk1 ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk1 ))]]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( sorti2 @ A )
| ~ ( sorti2 @ B )
| ( ( j @ ( op2 @ A @ B ) )
!= ( j @ sk1 ) )
| ( ( op1 @ ( j @ A ) @ ( j @ B ) )
!= ( op1 @ ( j @ sk1 ) @ ( j @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[15,49]) ).
thf(127,plain,
( ~ ( sorti2 @ sk1 )
| ~ ( sorti2 @ sk1 )
| ( ( j @ ( op2 @ sk1 @ sk1 ) )
!= ( j @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(130,plain,
( ~ ( sorti2 @ sk1 )
| ( ( j @ ( op2 @ sk1 @ sk1 ) )
!= ( j @ sk1 ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(32,plain,
( ( op2 @ sk1 @ sk1 )
= sk1 ),
inference(cnf,[status(esa)],[31]) ).
thf(34,plain,
( ( op2 @ sk1 @ sk1 )
= sk1 ),
inference(lifteq,[status(thm)],[32]) ).
thf(141,plain,
( ~ $true
| ( ( j @ sk1 )
!= ( j @ sk1 ) ) ),
inference(rewrite,[status(thm)],[130,33,34]) ).
thf(142,plain,
$false,
inference(simp,[status(thm)],[141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG201+1 : TPTP v8.1.2. Released v2.7.0.
% 0.09/0.11 % Command : run_Leo-III %s %d
% 0.10/0.30 % Computer : n004.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 6 23:02:24 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.95/0.89 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.07 % [INFO] Parsing done (178ms).
% 1.29/1.09 % [INFO] Running in sequential loop mode.
% 1.75/1.41 % [INFO] nitpick registered as external prover.
% 1.75/1.42 % [INFO] Scanning for conjecture ...
% 1.91/1.50 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 2.00/1.53 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.09/1.54 % [INFO] Problem is first-order (TPTP FOF).
% 2.09/1.55 % [INFO] Type checking passed.
% 2.09/1.55 % [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 ...
% 4.44/2.32 % [INFO] Killing All external provers ...
% 4.44/2.32 % Time passed: 1866ms (effective reasoning time: 1227ms)
% 4.44/2.32 % 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)>
% 4.44/2.32 % Axioms used in derivation (2): ax4, ax3
% 4.44/2.32 % No. of inferences in proof: 28
% 4.44/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1866 ms resp. 1227 ms w/o parsing
% 4.44/2.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.44/2.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------