TSTP Solution File: NUM693_8 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM693_8 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 10:45:15 EDT 2024
% Result : Theorem 2.85s 1.71s
% Output : Refutation 2.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 33 ( 15 unt; 7 typ; 0 def)
% Number of atoms : 40 ( 30 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 25 ~; 6 |; 0 &; 53 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 0 ^ 26 !; 1 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(x_type,type,
x: nat ).
thf(more_type,type,
more: nat > nat > $o ).
thf(n_1_type,type,
n_1: nat ).
thf(suc_type,type,
suc: nat > nat ).
thf(pl_type,type,
pl: nat > nat > nat ).
thf(sk1_type,type,
sk1: nat > nat ).
thf(4,axiom,
! [A: nat] :
( ( A != n_1 )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz3) ).
thf(12,plain,
! [A: nat] :
( ( A != n_1 )
=> ~ ! [B: nat] :
( A
!= ( suc @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [A: nat] :
( ( A != n_1 )
=> ~ ~ ? [B: nat] :
( A
= ( suc @ B ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [A: nat] :
( ( A = n_1 )
| ( A
= ( suc @ ( sk1 @ A ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [A: nat] :
( ( A = n_1 )
| ( ( suc @ ( sk1 @ A ) )
= A ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(5,axiom,
! [A: nat,B: nat] : ( more @ ( pl @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz18) ).
thf(16,plain,
! [A: nat,B: nat] : ( more @ ( pl @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [B: nat,A: nat] : ( more @ ( pl @ A @ B ) @ A ),
inference(cnf,[status(esa)],[16]) ).
thf(1,conjecture,
( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz24) ).
thf(2,negated_conjecture,
~ ( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ~ ( more @ x @ n_1 )
=> ( x = n_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
~ ( more @ x @ n_1 ),
inference(cnf,[status(esa)],[7]) ).
thf(23,plain,
! [B: nat,A: nat] :
( ( more @ ( pl @ A @ B ) @ A )
!= ( more @ x @ n_1 ) ),
inference(paramod_ordered,[status(thm)],[17,9]) ).
thf(24,plain,
! [B: nat,A: nat] :
( ( ( pl @ A @ B )
!= x )
| ( A != n_1 ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [A: nat] :
( ( pl @ n_1 @ A )
!= x ),
inference(simp,[status(thm)],[24]) ).
thf(6,axiom,
! [A: nat] :
( ( suc @ A )
= ( pl @ n_1 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz4g) ).
thf(18,plain,
! [A: nat] :
( ( suc @ A )
= ( pl @ n_1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [A: nat] :
( ( suc @ A )
= ( pl @ n_1 @ A ) ),
inference(cnf,[status(esa)],[18]) ).
thf(20,plain,
! [A: nat] :
( ( pl @ n_1 @ A )
= ( suc @ A ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(26,plain,
! [A: nat] :
( ( suc @ A )
!= x ),
inference(rewrite,[status(thm)],[25,20]) ).
thf(32,plain,
! [B: nat,A: nat] :
( ( A = n_1 )
| ( A != x )
| ( ( suc @ ( sk1 @ A ) )
!= ( suc @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,26]) ).
thf(33,plain,
! [A: nat] :
( ( A = n_1 )
| ( A != x ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( C )),bind(B,$thf( sk1 @ C ))]]) ).
thf(35,plain,
n_1 = x,
inference(simp,[status(thm)],[33]) ).
thf(8,plain,
x != n_1,
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
n_1 != x,
inference(lifteq,[status(thm)],[8]) ).
thf(37,plain,
$false,
inference(simplifyReflect,[status(thm)],[35,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM693_8 : TPTP v8.1.2. Released v8.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n025.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 19:43:24 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.01 % [INFO] Parsing done (124ms).
% 1.29/1.02 % [INFO] Running in sequential loop mode.
% 1.70/1.22 % [INFO] nitpick registered as external prover.
% 1.70/1.23 % [INFO] Scanning for conjecture ...
% 1.76/1.28 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.76/1.30 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.76/1.31 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.76/1.31 % [INFO] Type checking passed.
% 1.76/1.32 % [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 ...
% 2.66/1.67 % [INFO] Killing All external provers ...
% 2.85/1.71 % Time passed: 1142ms (effective reasoning time: 649ms)
% 2.85/1.71 % 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)>
% 2.85/1.71 % Axioms used in derivation (3): satz3, satz18, satz4g
% 2.85/1.71 % No. of inferences in proof: 26
% 2.85/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1142 ms resp. 649 ms w/o parsing
% 2.85/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.85/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------