TSTP Solution File: COL065-1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : COL065-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 07:29:27 EDT 2024
% Result : Unsatisfiable 32.85s 6.70s
% Output : Refutation 32.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 14 ( 7 unt; 7 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 78 ( 2 ~; 0 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 ^ 12 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(apply_type,type,
apply: $i > $i > $i ).
thf(f_type,type,
f: $i > $i ).
thf(g_type,type,
g: $i > $i ).
thf(h_type,type,
h: $i > $i ).
thf(i_type,type,
i: $i > $i ).
thf(b_type,type,
b: $i ).
thf(t_type,type,
t: $i ).
thf(1,negated_conjecture,
! [A: $i] :
( ( apply @ ( apply @ ( apply @ ( apply @ A @ ( f @ A ) ) @ ( g @ A ) ) @ ( h @ A ) ) @ ( i @ A ) )
!= ( apply @ ( apply @ ( f @ A ) @ ( i @ A ) ) @ ( apply @ ( g @ A ) @ ( h @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_combinator) ).
thf(4,plain,
! [A: $i] :
( ( apply @ ( apply @ ( apply @ ( apply @ A @ ( f @ A ) ) @ ( g @ A ) ) @ ( h @ A ) ) @ ( i @ A ) )
!= ( apply @ ( apply @ ( f @ A ) @ ( i @ A ) ) @ ( apply @ ( g @ A ) @ ( h @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
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(7,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(3,axiom,
! [B: $i,A: $i] :
( ( apply @ ( apply @ t @ A ) @ B )
= ( apply @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( apply @ ( apply @ t @ A ) @ B )
= ( apply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11798,plain,
$false,
inference(e,[status(thm)],[4,7,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL065-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 14:01:24 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (102ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.66/1.17 % [INFO] eprover registered as external prover.
% 1.66/1.17 % [INFO] cvc4 registered as external prover.
% 1.66/1.17 % [INFO] Scanning for conjecture ...
% 1.66/1.22 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.87/1.25 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.87/1.25 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.25 % [INFO] Type checking passed.
% 1.87/1.26 % [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 ...
% 32.85/6.70 % External prover 'e' found a proof!
% 32.85/6.70 % [INFO] Killing All external provers ...
% 32.85/6.70 % Time passed: 6184ms (effective reasoning time: 5738ms)
% 32.85/6.70 % 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)>
% 32.85/6.70 % Axioms used in derivation (2): b_definition, t_definition
% 32.85/6.70 % No. of inferences in proof: 7
% 32.85/6.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6184 ms resp. 5738 ms w/o parsing
% 32.85/6.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.85/6.72 % [INFO] Killing All external provers ...
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