TSTP Solution File: COL048-1 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : COL048-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n026.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 04:49:38 EDT 2024
% Result : Unsatisfiable 277.52s 52.96s
% Output : Refutation 277.52s
% 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(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
= ( apply @ A @ ( apply @ B @ C ) ) ),
file('/export/starexec/sandbox2/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(4,axiom,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_definition) ).
thf(12,plain,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,plain,
! [A: $i] :
( ( apply @ m @ A )
= ( apply @ A @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( apply @ A @ ( apply @ B @ C ) )
= ( apply @ m @ D ) )
| ( ( apply @ ( apply @ ( apply @ b @ A ) @ B ) @ C )
!= ( apply @ D @ D ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
= ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[194:[bind(A,$thf( L )),bind(B,$thf( J )),bind(C,$thf( apply @ ( apply @ b @ L ) @ J )),bind(D,$thf( apply @ ( apply @ b @ L ) @ J ))]]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
= ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(1,negated_conjecture,
! [A: $i] :
( A
!= ( apply @ combinator @ A ) ),
file('/export/starexec/sandbox2/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)],[13,7]) ).
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)],[13,16]) ).
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(140558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( apply @ m @ ( apply @ ( apply @ b @ B ) @ A ) )
!= ( apply @ m @ C ) )
| ( ( apply @ B @ ( apply @ A @ ( apply @ ( apply @ b @ B ) @ A ) ) )
!= ( apply @ combinator @ ( apply @ m @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,28]) ).
thf(140559,plain,
( ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) )
!= ( apply @ m @ ( apply @ ( apply @ b @ combinator ) @ m ) ) ),
inference(pattern_uni,[status(thm)],[140558:[bind(A,$thf( m )),bind(B,$thf( combinator )),bind(C,$thf( apply @ ( apply @ b @ combinator ) @ m ))]]) ).
thf(144209,plain,
$false,
inference(simp,[status(thm)],[140559]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : COL048-1 : TPTP v8.2.0. Released v1.0.0.
% 0.10/0.12 % Command : run_Leo-III %s %d SAT
% 0.11/0.33 % Computer : n026.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Jun 18 15:36:40 EDT 2024
% 0.11/0.33 % CPUTime :
% 1.12/1.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.21 % [INFO] Parsing done (162ms).
% 1.50/1.23 % [INFO] Running in sequential loop mode.
% 2.04/1.63 % [INFO] nitpick registered as external prover.
% 2.04/1.64 % [INFO] Scanning for conjecture ...
% 2.21/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.21/1.76 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.21/1.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.77 % [INFO] Type checking passed.
% 2.39/1.78 % [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 ...
% 277.52/52.95 % [INFO] Killing All external provers ...
% 277.52/52.95 % Time passed: 52430ms (effective reasoning time: 51714ms)
% 277.52/52.96 % Axioms used in derivation (2): b_definition, m_definition
% 277.52/52.96 % No. of inferences in proof: 20
% 277.52/52.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 52430 ms resp. 51714 ms w/o parsing
% 277.52/52.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 277.52/52.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------