TSTP Solution File: COL021-1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : COL021-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n014.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 Jun 24 04:49:33 EDT 2024
% Result : Unsatisfiable 34.43s 5.98s
% Output : Refutation 34.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 16 unt; 4 typ; 0 def)
% Number of atoms : 24 ( 23 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 170 ( 14 ~; 4 |; 0 &; 152 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 33 ( 0 ^ 33 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_type,type,
apply: $i > $i > $i ).
thf(combinator_type,type,
combinator: $i ).
thf(b_type,type,
b: $i ).
thf(m_type,type,
m: $i ).
thf(3,axiom,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_definition) ).
thf(10,plain,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,plain,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( apply @ m @ A )
= ( apply @ B @ ( apply @ C @ D ) ) )
| ( ( apply @ A @ A )
!= ( apply @ ( apply @ ( apply @ b @ B ) @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[11,9]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) )
= ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( apply @ ( apply @ b @ L ) @ J )),bind(B,$thf( L )),bind(C,$thf( J )),bind(D,$thf( apply @ ( apply @ b @ L ) @ J ))]]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) )
= ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(1,negated_conjecture,
! [A: $i] :
( A
!= ( apply @ combinator @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
thf(5,plain,
! [A: $i] :
( A
!= ( apply @ combinator @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,plain,
! [A: $i] :
( A
!= ( apply @ combinator @ A ) ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
! [A: $i] :
( ( apply @ combinator @ A )
!= A ),
inference(lifteq,[status(thm)],[6]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( apply @ A @ A )
!= B )
| ( ( apply @ m @ A )
!= ( apply @ combinator @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,7]) ).
thf(16,plain,
! [A: $i] :
( ( apply @ m @ A )
!= ( apply @ combinator @ ( apply @ A @ A ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( apply @ combinator @ ( apply @ m @ A ) )
!= ( apply @ m @ B ) )
| ( ( apply @ A @ A )
!= ( apply @ B @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,16]) ).
thf(28,plain,
! [A: $i] :
( ( apply @ combinator @ ( apply @ m @ A ) )
!= ( apply @ m @ A ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(10214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) )
!= ( apply @ m @ C ) )
| ( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
!= ( apply @ combinator @ ( apply @ m @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[86,28]) ).
thf(10215,plain,
( ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) )
!= ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) ) ),
inference(pattern_uni,[status(thm)],[10214:[bind(A,$thf( m )),bind(B,$thf( combinator )),bind(C,$thf( apply @ ( apply @ b @ combinator ) @ m ))]]) ).
thf(11521,plain,
$false,
inference(simp,[status(thm)],[10215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL021-1 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 15:47:10 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.87/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.95 % [INFO] Parsing done (96ms).
% 1.18/0.96 % [INFO] Running in sequential loop mode.
% 1.45/1.16 % [INFO] nitpick registered as external prover.
% 1.45/1.16 % [INFO] Scanning for conjecture ...
% 1.71/1.21 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.80/1.23 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 1.81/1.24 % [INFO] Problem is propositional (TPTP CNF).
% 1.81/1.24 % [INFO] Type checking passed.
% 1.81/1.24 % [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 ...
% 34.43/5.96 % [INFO] Killing All external provers ...
% 34.43/5.98 % Time passed: 5458ms (effective reasoning time: 5016ms)
% 34.43/5.98 % Axioms used in derivation (2): m_definition, b_definition
% 34.43/5.98 % No. of inferences in proof: 20
% 34.43/5.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 5458 ms resp. 5016 ms w/o parsing
% 34.43/6.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 34.43/6.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------