TSTP Solution File: NUM670_8 by Leo-III-SAT---1.7.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : NUM670_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 01:35:45 EDT 2024
% Result : Theorem 6.29s 2.51s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 27 unt; 6 typ; 0 def)
% Number of atoms : 35 ( 34 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 196 ( 28 ~; 4 |; 0 &; 164 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 44 ( 0 ^ 42 !; 2 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(y_type,type,
y: nat ).
thf(z_type,type,
z: nat ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(sk1_type,type,
sk1: nat ).
thf(3,axiom,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(12,plain,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
~ ! [A: nat] :
( x
!= ( pl @ y @ A ) ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(14,plain,
~ ~ ? [A: nat] :
( x
= ( pl @ y @ A ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
( x
= ( pl @ y @ sk1 ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
( ( pl @ y @ sk1 )
= x ),
inference(lifteq,[status(thm)],[15]) ).
thf(5,axiom,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz6) ).
thf(18,plain,
! [A: nat,B: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( pl @ A @ B )
= ( pl @ B @ A ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(57,plain,
! [B: nat,A: nat] :
( ( ( pl @ B @ A )
= x )
| ( ( pl @ y @ sk1 )
!= ( pl @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,20]) ).
thf(58,plain,
( ( pl @ sk1 @ y )
= x ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( y )),bind(B,$thf( sk1 ))]]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( pl @ ( pl @ A @ B ) @ C )
= ( pl @ A @ ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz5) ).
thf(21,plain,
! [A: nat,B: nat,C: nat] :
( ( pl @ ( pl @ A @ B ) @ C )
= ( pl @ A @ ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
! [C: nat,B: nat,A: nat] :
( ( pl @ ( pl @ A @ B ) @ C )
= ( pl @ A @ ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [C: nat,B: nat,A: nat] :
( ( pl @ ( pl @ A @ B ) @ C )
= ( pl @ A @ ( pl @ B @ C ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(114,plain,
! [C: nat,B: nat,A: nat] :
( ( ( pl @ x @ C )
= ( pl @ A @ ( pl @ B @ C ) ) )
| ( ( pl @ sk1 @ y )
!= ( pl @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[58,23]) ).
thf(115,plain,
! [A: nat] :
( ( pl @ sk1 @ ( pl @ y @ A ) )
= ( pl @ x @ A ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( sk1 )),bind(B,$thf( y ))]]) ).
thf(126,plain,
! [A: nat] :
( ( pl @ sk1 @ ( pl @ y @ A ) )
= ( pl @ x @ A ) ),
inference(simp,[status(thm)],[115]) ).
thf(1,conjecture,
~ ! [A: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(2,negated_conjecture,
~ ~ ! [A: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ~ ! [A: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ A ) ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
~ ? [A: nat] :
( ( pl @ x @ z )
= ( pl @ ( pl @ y @ z ) @ A ) ),
inference(miniscope,[status(thm)],[8]) ).
thf(10,plain,
! [A: nat] :
( ( pl @ x @ z )
!= ( pl @ ( pl @ y @ z ) @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
! [A: nat] :
( ( pl @ ( pl @ y @ z ) @ A )
!= ( pl @ x @ z ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(53,plain,
! [C: nat,B: nat,A: nat] :
( ( ( pl @ A @ B )
!= ( pl @ x @ z ) )
| ( ( pl @ B @ A )
!= ( pl @ ( pl @ y @ z ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(54,plain,
! [A: nat] :
( ( pl @ A @ ( pl @ y @ z ) )
!= ( pl @ x @ z ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( pl @ y @ z )),bind(C,$thf( A ))]]) ).
thf(404,plain,
! [B: nat,A: nat] :
( ( ( pl @ x @ A )
!= ( pl @ x @ z ) )
| ( ( pl @ sk1 @ ( pl @ y @ A ) )
!= ( pl @ B @ ( pl @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[126,54]) ).
thf(405,plain,
( ( pl @ x @ z )
!= ( pl @ x @ z ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( z )),bind(B,$thf( sk1 ))]]) ).
thf(470,plain,
$false,
inference(simp,[status(thm)],[405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM670_8 : TPTP v8.2.0. Released v8.0.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n025.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 06:09:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.77/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.07/0.94 % [INFO] Parsing done (110ms).
% 1.07/0.95 % [INFO] Running in sequential loop mode.
% 1.47/1.19 % [INFO] nitpick registered as external prover.
% 1.47/1.20 % [INFO] Scanning for conjecture ...
% 1.57/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.57/1.31 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.73/1.32 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.73/1.32 % [INFO] Type checking passed.
% 1.73/1.33 % [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 ...
% 6.29/2.50 % [INFO] Killing All external provers ...
% 6.29/2.51 % Time passed: 2034ms (effective reasoning time: 1548ms)
% 6.29/2.51 % 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)>
% 6.29/2.51 % Axioms used in derivation (3): m, satz6, satz5
% 6.29/2.51 % No. of inferences in proof: 31
% 6.29/2.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2034 ms resp. 1548 ms w/o parsing
% 6.29/2.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.29/2.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------