TSTP Solution File: NUM666^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 3.94s 1.93s
% Output : Refutation 3.94s
% 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 : 10 ( 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(some_type,type,
some: ( nat > $o ) > $o ).
thf(diffprop_type,type,
diffprop: nat > nat > nat > $o ).
thf(moreis_type,type,
moreis: nat > nat > $o ).
thf(lessis_type,type,
lessis: nat > nat > $o ).
thf(3,axiom,
some @ ( diffprop @ x @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(8,plain,
some @ ( diffprop @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: nat,B: nat,C: nat] :
( ( lessis @ A @ B )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16a) ).
thf(10,plain,
! [A: nat,B: nat,C: nat] :
( ( lessis @ A @ B )
=> ( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,plain,
! [A: nat,B: nat] :
( ( lessis @ A @ B )
=> ! [C: nat] :
( ( some @ ( diffprop @ C @ B ) )
=> ( some @ ( diffprop @ C @ A ) ) ) ),
inference(miniscope,[status(thm)],[10]) ).
thf(12,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( lessis @ A @ B )
| ~ ( some @ ( diffprop @ C @ B ) )
| ( some @ ( diffprop @ C @ A ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(1,conjecture,
some @ ( diffprop @ x @ z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz16d) ).
thf(2,negated_conjecture,
~ ( some @ ( diffprop @ x @ z ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( some @ ( diffprop @ x @ z ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(35,plain,
! [C: nat,B: nat,A: nat] :
( ~ ( lessis @ A @ B )
| ~ ( some @ ( diffprop @ C @ B ) )
| ( ( some @ ( diffprop @ C @ A ) )
!= ( some @ ( diffprop @ x @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,7]) ).
thf(36,plain,
! [A: nat] :
( ~ ( lessis @ z @ A )
| ~ ( some @ ( diffprop @ x @ A ) ) ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( z )),bind(B,$thf( B )),bind(C,$thf( x ))]]) ).
thf(40,plain,
! [A: nat] :
( ~ ( lessis @ z @ A )
| ~ ( some @ ( diffprop @ x @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(61,plain,
! [A: nat] :
( ~ ( lessis @ z @ A )
| ( ( some @ ( diffprop @ x @ y ) )
!= ( some @ ( diffprop @ x @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,40]) ).
thf(62,plain,
~ ( lessis @ z @ y ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( y ))]]) ).
thf(4,axiom,
moreis @ y @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n) ).
thf(9,plain,
moreis @ y @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz13) ).
thf(13,plain,
! [A: nat,B: nat] :
( ( moreis @ A @ B )
=> ( lessis @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [B: nat,A: nat] :
( ~ ( moreis @ A @ B )
| ( lessis @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(21,plain,
! [B: nat,A: nat] :
( ( lessis @ B @ A )
| ( ( moreis @ y @ z )
!= ( moreis @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,14]) ).
thf(22,plain,
lessis @ z @ y,
inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( y )),bind(B,$thf( z ))]]) ).
thf(63,plain,
~ $true,
inference(rewrite,[status(thm)],[62,22]) ).
thf(64,plain,
$false,
inference(simp,[status(thm)],[63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM666^1 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.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 19:51:24 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.94/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/0.99 % [INFO] Parsing done (119ms).
% 1.22/1.00 % [INFO] Running in sequential loop mode.
% 1.77/1.24 % [INFO] nitpick registered as external prover.
% 1.77/1.24 % [INFO] Scanning for conjecture ...
% 1.77/1.30 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.77/1.33 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.77/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.34 % [INFO] Type checking passed.
% 2.06/1.34 % [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 ...
% 3.94/1.93 % [INFO] Killing All external provers ...
% 3.94/1.93 % Time passed: 1400ms (effective reasoning time: 923ms)
% 3.94/1.93 % 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)>
% 3.94/1.93 % Axioms used in derivation (4): m, satz16a, n, satz13
% 3.94/1.93 % No. of inferences in proof: 23
% 3.94/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1400 ms resp. 923 ms w/o parsing
% 3.94/1.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.94/1.96 % [INFO] Killing All external provers ...
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