TSTP Solution File: NUM830^5 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 10:45:50 EDT 2024
% Result : Theorem 4.36s 2.22s
% Output : Refutation 4.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 31 unt; 9 typ; 4 def)
% Number of atoms : 60 ( 47 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 334 ( 23 ~; 3 |; 9 &; 296 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 33 ( 0 ^ 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(n_type,type,
n: $tType ).
thf(c0_type,type,
c0: n ).
thf(cS_type,type,
cS: n > n ).
thf(c_plus_type,type,
c_plus: n > n > n ).
thf(c_star_type,type,
c_star: n > n > n ).
thf(cPA_1_type,type,
cPA_1: $o ).
thf(cPA_1_def,definition,
( cPA_1
= ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A ) ) ) ).
thf(cPA_2_type,type,
cPA_2: $o ).
thf(cPA_2_def,definition,
( cPA_2
= ( ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ) ) ) ).
thf(cPA_3_type,type,
cPA_3: $o ).
thf(cPA_3_def,definition,
( cPA_3
= ( ! [A: n] :
( ( c_star @ A @ c0 )
= c0 ) ) ) ).
thf(cPA_4_type,type,
cPA_4: $o ).
thf(cPA_4_def,definition,
( cPA_4
= ( ! [A: n,B: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ) ) ) ).
thf(1,conjecture,
( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPA_THM1) ).
thf(2,negated_conjecture,
~ ( ( cPA_1
& cPA_2
& cPA_3
& cPA_4 )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: n] :
( ( c_plus @ A @ c0 )
= A )
& ! [A: n,B: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) )
& ! [A: n] :
( ( c_star @ A @ c0 )
= c0 )
& ! [A: n,B: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ) )
=> ( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,plain,
! [A: n] :
( ( c_plus @ A @ c0 )
= A ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [A: n] :
( ( c_plus @ A @ c0 )
= A ),
inference(lifteq,[status(thm)],[8]) ).
thf(4,plain,
! [A: n] :
( ( c_star @ A @ c0 )
= c0 ),
inference(cnf,[status(esa)],[3]) ).
thf(15,plain,
! [A: n] :
( ( c_star @ A @ c0 )
= c0 ),
inference(lifteq,[status(thm)],[4]) ).
thf(16,plain,
! [A: n] :
( ( c_star @ A @ c0 )
= c0 ),
inference(simp,[status(thm)],[15]) ).
thf(6,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(12,plain,
! [B: n,A: n] :
( ( c_plus @ A @ ( cS @ B ) )
= ( cS @ ( c_plus @ A @ B ) ) ),
inference(simp,[status(thm)],[11]) ).
thf(7,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(20,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[13,12]) ).
thf(5,plain,
! [B: n,A: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [B: n,A: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
! [B: n,A: n] :
( ( c_star @ A @ ( cS @ B ) )
= ( c_plus @ ( c_star @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[9]) ).
thf(48,plain,
( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[20,10,12]) ).
thf(52,plain,
! [B: n,A: n] :
( ( ( cS @ ( c_plus @ A @ B ) )
!= ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ) )
| ( ( c_plus @ A @ ( cS @ B ) )
!= ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,48]) ).
thf(53,plain,
( ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( c_plus @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) )),bind(B,$thf( cS @ c0 ))]]) ).
thf(59,plain,
( ( cS @ ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ ( cS @ c0 ) ) ) ) ),
inference(rewrite,[status(thm)],[53,12,14]) ).
thf(60,plain,
( ( cS @ ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) @ c0 ) )
!= ( cS @ ( cS @ ( cS @ c0 ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(77,plain,
( ( cS @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ ( cS @ c0 ) ) ) ),
inference(rewrite,[status(thm)],[60,14]) ).
thf(78,plain,
( ( c_star @ ( cS @ ( cS @ c0 ) ) @ ( cS @ c0 ) )
!= ( cS @ ( cS @ c0 ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(87,plain,
( ( c_plus @ ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ c0 ) ) ),
inference(rewrite,[status(thm)],[78,10]) ).
thf(92,plain,
! [A: n] :
( ( ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ c0 ) ) )
| ( ( c_star @ A @ c0 )
!= ( c_star @ ( cS @ ( cS @ c0 ) ) @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[16,87]) ).
thf(93,plain,
( ( c_plus @ c0 @ ( cS @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ c0 ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( cS @ ( cS @ c0 ) ))]]) ).
thf(98,plain,
( ( cS @ ( c_plus @ c0 @ ( cS @ c0 ) ) )
!= ( cS @ ( cS @ c0 ) ) ),
inference(rewrite,[status(thm)],[93,12]) ).
thf(99,plain,
( ( c_plus @ c0 @ ( cS @ c0 ) )
!= ( cS @ c0 ) ),
inference(simp,[status(thm)],[98]) ).
thf(109,plain,
( ( cS @ ( c_plus @ c0 @ c0 ) )
!= ( cS @ c0 ) ),
inference(rewrite,[status(thm)],[99,12]) ).
thf(111,plain,
! [A: n] :
( ( ( cS @ A )
!= ( cS @ c0 ) )
| ( ( c_plus @ A @ c0 )
!= ( c_plus @ c0 @ c0 ) ) ),
inference(paramod_ordered,[status(thm)],[14,109]) ).
thf(112,plain,
( ( cS @ c0 )
!= ( cS @ c0 ) ),
inference(pattern_uni,[status(thm)],[111:[bind(A,$thf( c0 ))]]) ).
thf(117,plain,
$false,
inference(simp,[status(thm)],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : NUM830^5 : TPTP v8.1.2. Bugfixed v5.3.0.
% 0.08/0.11 % Command : run_Leo-III %s %d
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 6 19:58:09 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.89/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/1.08 % [INFO] Parsing done (177ms).
% 1.34/1.10 % [INFO] Running in sequential loop mode.
% 1.72/1.36 % [INFO] nitpick registered as external prover.
% 1.72/1.37 % [INFO] Scanning for conjecture ...
% 1.90/1.44 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ...
% 1.96/1.46 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.96/1.46 % [INFO] Problem is higher-order (TPTP THF).
% 1.96/1.46 % [INFO] Type checking passed.
% 1.96/1.46 % [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 ...
% 4.36/2.21 % [INFO] Killing All external provers ...
% 4.36/2.21 % Time passed: 1756ms (effective reasoning time: 1109ms)
% 4.36/2.21 % 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)>
% 4.36/2.21 % Axioms used in derivation (0):
% 4.36/2.21 % No. of inferences in proof: 33
% 4.36/2.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1756 ms resp. 1109 ms w/o parsing
% 4.36/2.27 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.36/2.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------