TSTP Solution File: NUM672^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM672^1 : 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 10:45:08 EDT 2024
% Result : Theorem 3.15s 1.80s
% Output : Refutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 32 ( 12 unt; 7 typ; 0 def)
% Number of atoms : 44 ( 3 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 152 ( 9 ~; 6 |; 0 &; 130 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 36 ( 0 ^ 36 !; 0 ?; 36 :)
% 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 > $o ).
thf(1,conjecture,
less @ ( pl @ x @ z ) @ ( pl @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19c) ).
thf(2,negated_conjecture,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( less @ ( pl @ x @ z ) @ ( pl @ y @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
less @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(8,plain,
less @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( less @ A @ B )
=> ( more @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz12) ).
thf(14,plain,
! [A: nat,B: nat] :
( ( less @ A @ B )
=> ( more @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [B: nat,A: nat] :
( ~ ( less @ A @ B )
| ( more @ B @ A ) ),
inference(cnf,[status(esa)],[14]) ).
thf(20,plain,
! [B: nat,A: nat] :
( ( more @ B @ A )
| ( ( less @ x @ y )
!= ( less @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,15]) ).
thf(21,plain,
more @ y @ x,
inference(pattern_uni,[status(thm)],[20:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19a) ).
thf(11,plain,
! [A: nat,B: nat,C: nat] :
( ( more @ A @ B )
=> ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ! [C: nat] : ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(13,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) ) ),
inference(cnf,[status(esa)],[12]) ).
thf(33,plain,
! [C: nat,B: nat,A: nat] :
( ( more @ ( pl @ A @ C ) @ ( pl @ B @ C ) )
| ( ( more @ y @ x )
!= ( more @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,13]) ).
thf(34,plain,
! [A: nat] : ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( y )),bind(B,$thf( x ))]]) ).
thf(35,plain,
! [A: nat] : ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) ),
inference(simp,[status(thm)],[34]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz11) ).
thf(9,plain,
! [A: nat,B: nat] :
( ( more @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [B: nat,A: nat] :
( ~ ( more @ A @ B )
| ( less @ B @ A ) ),
inference(cnf,[status(esa)],[9]) ).
thf(36,plain,
! [C: nat,B: nat,A: nat] :
( ( less @ C @ B )
| ( ( more @ ( pl @ y @ A ) @ ( pl @ x @ A ) )
!= ( more @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,10]) ).
thf(37,plain,
! [A: nat] : ( less @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( G )),bind(B,$thf( pl @ y @ G )),bind(C,$thf( pl @ x @ G ))]]) ).
thf(40,plain,
! [A: nat] : ( less @ ( pl @ x @ A ) @ ( pl @ y @ A ) ),
inference(simp,[status(thm)],[37]) ).
thf(42,plain,
~ $true,
inference(rewrite,[status(thm)],[7,40]) ).
thf(43,plain,
$false,
inference(simp,[status(thm)],[42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM672^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 19:25:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/1.04 % [INFO] Parsing done (128ms).
% 1.22/1.05 % [INFO] Running in sequential loop mode.
% 1.71/1.27 % [INFO] nitpick registered as external prover.
% 1.71/1.28 % [INFO] Scanning for conjecture ...
% 1.71/1.33 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.95/1.35 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.95/1.36 % [INFO] Problem is higher-order (TPTP THF).
% 1.95/1.37 % [INFO] Type checking passed.
% 1.95/1.37 % [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 ...
% 3.15/1.79 % [INFO] Killing All external provers ...
% 3.15/1.80 % Time passed: 1254ms (effective reasoning time: 737ms)
% 3.15/1.80 % 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)>
% 3.15/1.80 % Axioms used in derivation (4): l, satz12, satz19a, satz11
% 3.15/1.80 % No. of inferences in proof: 25
% 3.15/1.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1254 ms resp. 737 ms w/o parsing
% 3.25/1.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.25/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------