TSTP Solution File: NUM663^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM663^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 10:45:05 EDT 2024
% Result : Theorem 2.59s 1.60s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 46 ( 10 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 102 ( 17 ~; 9 |; 0 &; 68 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 17 ( 0 ^ 17 !; 0 ?; 17 :)
% 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(less_type,type,
less: nat > nat > $o ).
thf(4,axiom,
less @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k) ).
thf(11,plain,
less @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz15) ).
thf(13,plain,
! [A: nat,B: nat,C: nat] :
( ( less @ A @ B )
=> ( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [A: nat,B: nat] :
( ( less @ A @ B )
=> ! [C: nat] :
( ( less @ B @ C )
=> ( less @ A @ C ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ~ ( less @ B @ C )
| ( less @ A @ C ) ),
inference(cnf,[status(esa)],[14]) ).
thf(27,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( less @ A @ C )
| ( ( less @ y @ z )
!= ( less @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,15]) ).
thf(28,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ( less @ A @ z ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1,conjecture,
less @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(2,negated_conjecture,
~ ( less @ x @ z ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( less @ x @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(45,plain,
! [A: nat] :
( ~ ( less @ A @ y )
| ( ( less @ A @ z )
!= ( less @ x @ z ) ) ),
inference(paramod_ordered,[status(thm)],[28,7]) ).
thf(46,plain,
~ ( less @ x @ y ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( x ))]]) ).
thf(3,axiom,
( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l) ).
thf(8,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[8]) ).
thf(10,plain,
( ( y = x )
| ( less @ x @ y ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(16,plain,
( ( less @ y @ z )
!= ( less @ x @ z ) ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(17,plain,
( ( y != x )
| ( z != z ) ),
inference(simp,[status(thm)],[16]) ).
thf(18,plain,
y != x,
inference(simp,[status(thm)],[17]) ).
thf(19,plain,
less @ x @ y,
inference(simplifyReflect,[status(thm)],[10,18]) ).
thf(61,plain,
~ $true,
inference(rewrite,[status(thm)],[46,19]) ).
thf(62,plain,
$false,
inference(simp,[status(thm)],[61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM663^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n015.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 19:31:54 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.97/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.96 % [INFO] Parsing done (114ms).
% 1.21/0.97 % [INFO] Running in sequential loop mode.
% 1.63/1.17 % [INFO] nitpick registered as external prover.
% 1.63/1.17 % [INFO] Scanning for conjecture ...
% 1.71/1.21 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.71/1.23 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.80/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.80/1.24 % [INFO] Type checking passed.
% 1.80/1.25 % [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 ...
% 2.59/1.59 % [INFO] Killing All external provers ...
% 2.59/1.59 % Time passed: 1070ms (effective reasoning time: 620ms)
% 2.59/1.59 % 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)>
% 2.59/1.60 % Axioms used in derivation (3): k, satz15, l
% 2.59/1.60 % No. of inferences in proof: 23
% 2.59/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1070 ms resp. 620 ms w/o parsing
% 2.78/1.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.78/1.67 % [INFO] Killing All external provers ...
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