TSTP Solution File: NUM656_8 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM656_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 10:45:03 EDT 2024
% Result : Theorem 2.52s 1.53s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 29 ( 8 unt; 5 typ; 0 def)
% Number of atoms : 56 ( 21 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 42 ~; 9 |; 0 &; 66 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 ^ 23 !; 0 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(y_type,type,
y: nat ).
thf(more_type,type,
more: nat > nat > $o ).
thf(less_type,type,
less: nat > nat > $o ).
thf(1,conjecture,
~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10g) ).
thf(2,negated_conjecture,
~ ~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ~ ( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( ~ ( less @ x @ y )
=> ( x = y ) ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( less @ x @ y )
| ( x = y ) ),
inference(cnf,[status(esa)],[7]) ).
thf(9,plain,
( ( y = x )
| ( less @ x @ y ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(3,axiom,
more @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(10,plain,
more @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: nat,B: nat] :
~ ( ( ( A = B )
=> ~ ( more @ A @ B ) )
=> ~ ~ ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz10b) ).
thf(12,plain,
! [A: nat,B: nat] :
~ ( ( ( A = B )
=> ~ ( more @ A @ B ) )
=> ( ( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ( ( less @ A @ B )
=> ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
~ ( ! [A: nat,B: nat] :
( ( A = B )
=> ~ ( more @ A @ B ) )
=> ( ! [A: nat,B: nat] :
( ( more @ A @ B )
=> ~ ( less @ A @ B ) )
=> ~ ! [A: nat,B: nat] :
( ( less @ A @ B )
=> ( A != B ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(15,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(19,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ~ ( less @ A @ B ) ),
inference(simp,[status(thm)],[15]) ).
thf(25,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( ( more @ x @ y )
!= ( more @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(26,plain,
~ ( less @ x @ y ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(27,plain,
( ( y = x )
| $false ),
inference(rewrite,[status(thm)],[9,26]) ).
thf(28,plain,
y = x,
inference(simp,[status(thm)],[27]) ).
thf(16,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( more @ A @ B ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(21,plain,
! [A: nat] :
~ ( more @ A @ A ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: nat] :
( ( more @ x @ y )
!= ( more @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[10,21]) ).
thf(23,plain,
! [A: nat] :
( ( x != A )
| ( y != A ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
y != x,
inference(simp,[status(thm)],[23]) ).
thf(29,plain,
$false,
inference(simplifyReflect,[status(thm)],[28,24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM656_8 : TPTP v8.1.2. Released v8.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n023.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 : Mon May 6 19:26:09 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.86/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.91 % [INFO] Parsing done (103ms).
% 1.11/0.92 % [INFO] Running in sequential loop mode.
% 1.52/1.12 % [INFO] nitpick registered as external prover.
% 1.52/1.13 % [INFO] Scanning for conjecture ...
% 1.71/1.17 % [INFO] Found a conjecture and 3 axioms. Running axiom selection ...
% 1.71/1.19 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.81/1.21 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.81/1.21 % [INFO] Type checking passed.
% 1.81/1.21 % [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 ...
% 2.52/1.53 % [INFO] Killing All external provers ...
% 2.52/1.53 % Time passed: 1004ms (effective reasoning time: 605ms)
% 2.52/1.53 % 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)>
% 2.52/1.53 % Axioms used in derivation (2): m, satz10b
% 2.52/1.53 % No. of inferences in proof: 24
% 2.52/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1004 ms resp. 605 ms w/o parsing
% 2.52/1.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.52/1.61 % [INFO] Killing All external provers ...
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