TSTP Solution File: GRP001^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : Mon May 20 21:02:53 EDT 2024
% Result : Theorem 30.50s 5.66s
% Output : Refutation 30.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 24 unt; 4 typ; 0 def)
% Number of atoms : 59 ( 58 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 278 ( 23 ~; 11 |; 9 &; 232 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 0 ^ 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(cP_type,type,
cP: $i > $i > $i ).
thf(e_type,type,
e: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( cP @ e @ A )
= A )
& ! [A: $i] :
( ( cP @ A @ e )
= A )
& ! [A: $i] :
( ( cP @ A @ A )
= e )
& ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ) )
=> ! [A: $i,B: $i] :
( ( cP @ A @ B )
= ( cP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_COMM2) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( cP @ e @ A )
= A )
& ! [A: $i] :
( ( cP @ A @ e )
= A )
& ! [A: $i] :
( ( cP @ A @ A )
= e )
& ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ) )
=> ! [A: $i,B: $i] :
( ( cP @ A @ B )
= ( cP @ B @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ( cP @ e @ A )
= A )
& ! [A: $i] :
( ( cP @ A @ e )
= A )
& ! [A: $i] :
( ( cP @ A @ A )
= e )
& ! [A: $i,B: $i,C: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ) )
=> ! [A: $i,B: $i] :
( ( cP @ A @ B )
= ( cP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,plain,
! [A: $i] :
( ( cP @ A @ A )
= e ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
! [A: $i] :
( ( cP @ A @ A )
= e ),
inference(lifteq,[status(thm)],[6]) ).
thf(11,plain,
! [A: $i] :
( ( cP @ A @ A )
= e ),
inference(simp,[status(thm)],[10]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( cP @ ( cP @ A @ B ) @ C )
= ( cP @ A @ ( cP @ B @ C ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cP @ e @ D )
= ( cP @ B @ ( cP @ C @ D ) ) )
| ( ( cP @ A @ A )
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[11,15]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( cP @ e @ B )
= ( cP @ A @ ( cP @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( cP @ e @ B )
= ( cP @ A @ ( cP @ A @ B ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(5,plain,
! [A: $i] :
( ( cP @ e @ A )
= A ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [A: $i] :
( ( cP @ e @ A )
= A ),
inference(lifteq,[status(thm)],[5]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( cP @ A @ ( cP @ A @ B ) )
= B ),
inference(rewrite,[status(thm)],[76,9]) ).
thf(4,plain,
( ( cP @ sk1 @ sk2 )
!= ( cP @ sk2 @ sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
( ( cP @ sk2 @ sk1 )
!= ( cP @ sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( cP @ A @ ( cP @ B @ C ) )
!= ( cP @ sk1 @ sk2 ) )
| ( ( cP @ ( cP @ A @ B ) @ C )
!= ( cP @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[15,16]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( ( cP @ B @ C )
!= sk2 )
| ( ( cP @ ( cP @ A @ B ) @ C )
!= ( cP @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( cP @ A @ B )
!= sk2 )
| ( ( cP @ ( cP @ sk1 @ A ) @ B )
!= ( cP @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(586,plain,
! [B: $i,A: $i] :
( ( ( cP @ A @ B )
!= sk2 )
| ( ( cP @ sk1 @ ( cP @ A @ B ) )
!= ( cP @ sk2 @ sk1 ) ) ),
inference(rewrite,[status(thm)],[78,15]) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cP @ C @ D )
!= sk2 )
| ( B
!= ( cP @ sk2 @ sk1 ) )
| ( ( cP @ A @ ( cP @ A @ B ) )
!= ( cP @ sk1 @ ( cP @ C @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[165,586]) ).
thf(600,plain,
! [A: $i] :
( ( ( cP @ sk1 @ A )
!= sk2 )
| ( A
!= ( cP @ sk2 @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( sk1 )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( B ))]]) ).
thf(702,plain,
( ( cP @ sk1 @ ( cP @ sk2 @ sk1 ) )
!= sk2 ),
inference(simp,[status(thm)],[600]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cP @ B @ ( cP @ C @ D ) )
= e )
| ( ( cP @ A @ A )
!= ( cP @ ( cP @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,15]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
= e ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( cP @ G @ H )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( cP @ G @ H ))]]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
= e ),
inference(simp,[status(thm)],[64]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( cP @ C @ e )
= D )
| ( ( cP @ A @ ( cP @ B @ ( cP @ A @ B ) ) )
!= ( cP @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[75,165]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( cP @ A @ e )
= ( cP @ B @ ( cP @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( cP @ H @ ( cP @ G @ H ) ))]]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( cP @ A @ e )
= ( cP @ B @ ( cP @ A @ B ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(7,plain,
! [A: $i] :
( ( cP @ A @ e )
= A ),
inference(cnf,[status(esa)],[3]) ).
thf(12,plain,
! [A: $i] :
( ( cP @ A @ e )
= A ),
inference(lifteq,[status(thm)],[7]) ).
thf(13,plain,
! [A: $i] :
( ( cP @ A @ e )
= A ),
inference(simp,[status(thm)],[12]) ).
thf(8881,plain,
! [B: $i,A: $i] :
( ( cP @ B @ ( cP @ A @ B ) )
= A ),
inference(rewrite,[status(thm)],[222,13]) ).
thf(8883,plain,
sk2 != sk2,
inference(rewrite,[status(thm)],[702,8881]) ).
thf(8884,plain,
$false,
inference(simp,[status(thm)],[8883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP001^5 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n010.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 05:47:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.97 % [INFO] Parsing done (102ms).
% 1.21/0.98 % [INFO] Running in sequential loop mode.
% 1.63/1.19 % [INFO] nitpick registered as external prover.
% 1.63/1.19 % [INFO] Scanning for conjecture ...
% 1.84/1.25 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.84/1.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.84/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.27 % [INFO] Type checking passed.
% 1.84/1.28 % [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 ...
% 30.50/5.66 % [INFO] Killing All external provers ...
% 30.50/5.66 % Time passed: 5127ms (effective reasoning time: 4674ms)
% 30.50/5.66 % 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)>
% 30.50/5.66 % Axioms used in derivation (0):
% 30.50/5.66 % No. of inferences in proof: 36
% 30.50/5.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5127 ms resp. 4674 ms w/o parsing
% 30.50/5.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 30.50/5.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------