TSTP Solution File: NUM682^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 10:45:11 EDT 2024
% Result : Theorem 4.71s 2.07s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 14 unt; 7 typ; 0 def)
% Number of atoms : 85 ( 24 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 260 ( 50 ~; 20 |; 0 &; 168 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 ^ 49 !; 0 ?; 49 :)
% 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(pl_type,type,
pl: nat > nat > nat ).
thf(more_type,type,
more: nat > nat > $o ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(22,plain,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(23,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ! [C: nat] : ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(3,axiom,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(10,plain,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
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/sandbox/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(164,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,19]) ).
thf(165,plain,
~ ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( pl @ x @ z )),bind(B,$thf( pl @ y @ z ))]]) ).
thf(338,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
!= ( more @ ( pl @ x @ z ) @ ( pl @ y @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,165]) ).
thf(339,plain,
~ ( more @ x @ y ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(8,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( more @ A @ B )
=> ( less @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz10a) ).
thf(30,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( more @ A @ B )
=> ( less @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( more @ A @ B )
| ( less @ A @ B ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: nat,A: nat] :
( ( A = B )
| ( more @ A @ B )
| ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(14,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( A != B ) ),
inference(cnf,[status(esa)],[13]) ).
thf(17,plain,
! [B: nat,A: nat] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(18,plain,
! [A: nat] :
~ ( less @ A @ A ),
inference(simp,[status(thm)],[17]) ).
thf(35,plain,
! [A: nat] :
( ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) )
!= ( less @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[10,18]) ).
thf(36,plain,
! [A: nat] :
( ( ( pl @ x @ z )
!= A )
| ( ( pl @ y @ z )
!= A ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
( ( pl @ y @ z )
!= ( pl @ x @ z ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
( ( y != x )
| ( z != z ) ),
inference(simp,[status(thm)],[37]) ).
thf(39,plain,
y != x,
inference(simp,[status(thm)],[38]) ).
thf(86,plain,
! [B: nat,A: nat] :
( ( more @ A @ B )
| ( less @ A @ B )
| ( A != x )
| ( B != y ) ),
inference(paramod_ordered,[status(thm)],[32,39]) ).
thf(87,plain,
! [A: nat] :
( ( more @ A @ y )
| ( less @ A @ y )
| ( A != x ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( A )),bind(B,$thf( y ))]]) ).
thf(119,plain,
( ( more @ x @ y )
| ( less @ x @ y ) ),
inference(simp,[status(thm)],[87]) ).
thf(1,conjecture,
less @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz20c) ).
thf(2,negated_conjecture,
~ ( less @ x @ y ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( less @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(303,plain,
( ( more @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[119,9]) ).
thf(304,plain,
more @ x @ y,
inference(simp,[status(thm)],[303]) ).
thf(364,plain,
~ $true,
inference(rewrite,[status(thm)],[339,304]) ).
thf(365,plain,
$false,
inference(simp,[status(thm)],[364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM682^1 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.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 19:58:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.85/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.06/0.92 % [INFO] Parsing done (114ms).
% 1.06/0.92 % [INFO] Running in sequential loop mode.
% 1.48/1.12 % [INFO] nitpick registered as external prover.
% 1.48/1.13 % [INFO] Scanning for conjecture ...
% 1.66/1.18 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.75/1.20 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.75/1.22 % [INFO] Problem is higher-order (TPTP THF).
% 1.75/1.22 % [INFO] Type checking passed.
% 1.75/1.22 % [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 ...
% 4.71/2.07 % [INFO] Killing All external provers ...
% 4.71/2.07 % Time passed: 1542ms (effective reasoning time: 1142ms)
% 4.71/2.07 % 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)>
% 4.71/2.07 % Axioms used in derivation (4): satz19a, l, satz10b, satz10a
% 4.71/2.07 % No. of inferences in proof: 37
% 4.71/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1542 ms resp. 1142 ms w/o parsing
% 4.77/2.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.77/2.10 % [INFO] Killing All external provers ...
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