TSTP Solution File: NUM665^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 10:45:06 EDT 2024
% Result : Theorem 3.83s 2.13s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 66 ( 3 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 136 ( 17 ~; 9 |; 0 &; 102 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 26 ( 0 ^ 26 !; 0 ?; 26 :)
% 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(moreis_type,type,
moreis: nat > nat > $o ).
thf(some_type,type,
some: ( nat > $o ) > $o ).
thf(diffprop_type,type,
diffprop: nat > nat > nat > $o ).
thf(lessis_type,type,
lessis: nat > nat > $o ).
thf(4,axiom,
some @ ( diffprop @ y @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(9,plain,
some @ ( diffprop @ y @ z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( lessis @ B @ C )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16b) ).
thf(10,plain,
! [A: nat,B: nat,C: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ( ( lessis @ B @ C )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,plain,
! [A: nat,B: nat] :
( ( some @ ( diffprop @ B @ A ) )
=> ! [C: nat] :
( ( lessis @ B @ C )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( some @ ( diffprop @ B @ A ) )
| ~ ( lessis @ B @ C )
| ( some @ ( diffprop @ C @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(1,conjecture,
some @ ( diffprop @ x @ z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz16c) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ x @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( some @ ( diffprop @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( some @ ( diffprop @ B @ A ) )
| ~ ( lessis @ B @ C )
| ( ( some @ ( diffprop @ C @ A ) )
!= ( some @ ( diffprop @ x @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(38,plain,
! [A: nat] :
( ~ ( some @ ( diffprop @ A @ z ) )
| ~ ( lessis @ A @ x ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( z )),bind(B,$thf( B )),bind(C,$thf( x ))]]) ).
thf(41,plain,
! [A: nat] :
( ~ ( some @ ( diffprop @ A @ z ) )
| ~ ( lessis @ A @ x ) ),
inference(simp,[status(thm)],[38]) ).
thf(57,plain,
! [A: nat] :
( ~ ( lessis @ A @ x )
| ( ( some @ ( diffprop @ y @ z ) )
!= ( some @ ( diffprop @ A @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,41]) ).
thf(58,plain,
~ ( lessis @ y @ x ),
inference(pattern_uni,[status(thm)],[57:[bind(A,$thf( y ))]]) ).
thf(3,axiom,
moreis @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(8,plain,
moreis @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz13) ).
thf(13,plain,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [B: nat,A: nat] :
( ~ ( moreis @ A @ B )
| ( lessis @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(21,plain,
! [B: nat,A: nat] :
( ( lessis @ B @ A )
| ( ( moreis @ x @ y )
!= ( moreis @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,14]) ).
thf(22,plain,
lessis @ y @ x,
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(65,plain,
~ $true,
inference(rewrite,[status(thm)],[58,22]) ).
thf(66,plain,
$false,
inference(simp,[status(thm)],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM665^1 : TPTP v8.1.2. Released v3.7.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 6 19:25:24 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.77/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.11/0.96 % [INFO] Parsing done (133ms).
% 1.11/0.97 % [INFO] Running in sequential loop mode.
% 1.53/1.27 % [INFO] nitpick registered as external prover.
% 1.53/1.28 % [INFO] Scanning for conjecture ...
% 1.74/1.35 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.74/1.38 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.90/1.40 % [INFO] Problem is higher-order (TPTP THF).
% 1.90/1.40 % [INFO] Type checking passed.
% 1.90/1.41 % [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 ...
% 3.83/2.13 % [INFO] Killing All external provers ...
% 3.83/2.13 % Time passed: 1638ms (effective reasoning time: 1152ms)
% 3.83/2.13 % 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)>
% 3.83/2.13 % Axioms used in derivation (4): n, satz16b, m, satz13
% 3.83/2.13 % No. of inferences in proof: 23
% 3.83/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1638 ms resp. 1152 ms w/o parsing
% 3.83/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/2.18 % [INFO] Killing All external provers ...
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