TSTP Solution File: SYO060^4 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO060^4 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 21 08:55:38 EDT 2024
% Result : Theorem 2.95s 1.70s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 21 ( 7 unt; 7 typ; 4 def)
% Number of atoms : 59 ( 4 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 84 ( 6 ~; 2 |; 2 &; 64 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 4 ^ 18 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
thf(irel_type,type,
irel: $i > $i > $o ).
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(iatom_def,definition,
( iatom
= ( ^ [A: $i > $o] : A ) ) ).
thf(inot_type,type,
inot: ( $i > $o ) > $i > $o ).
thf(inot_def,definition,
( inot
= ( ^ [A: $i > $o] : ( mnot @ ( mbox_s4 @ A ) ) ) ) ).
thf(ior_type,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(ior_def,definition,
( ior
= ( ^ [A: $i > $o,B: $i > $o] : ( mor @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(ivalid_def,definition,
( ivalid
= ( '!' @ $i ) ) ).
thf(a_type,type,
a: $i > $o ).
thf(b_type,type,
b: $i > $o ).
thf(1,conjecture,
ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ( irel @ A @ B )
=> ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( b @ C ) ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( a @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] : ( irel @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom) ).
thf(12,plain,
! [A: $i] : ( irel @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_axiom) ).
thf(14,plain,
! [A: $i,B: $i,C: $i] :
( ( ( irel @ A @ B )
& ( irel @ B @ C ) )
=> ( irel @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(16,plain,
! [A: $i] :
( ! [B: $i] :
( ( irel @ A @ B )
=> ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( a @ C ) ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( b @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[6,12,14,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO060^4 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n025.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 20 09:59:24 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.00 % [INFO] Parsing done (129ms).
% 1.46/1.01 % [INFO] Running in sequential loop mode.
% 1.82/1.23 % [INFO] eprover registered as external prover.
% 1.82/1.23 % [INFO] cvc4 registered as external prover.
% 1.90/1.24 % [INFO] Scanning for conjecture ...
% 1.90/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 1.90/1.33 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.20/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.34 % [INFO] Type checking passed.
% 2.20/1.34 % [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 ...
% 2.95/1.70 % External prover 'e' found a proof!
% 2.95/1.70 % [INFO] Killing All external provers ...
% 2.95/1.70 % Time passed: 1164ms (effective reasoning time: 685ms)
% 2.95/1.70 % 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)>
% 2.95/1.70 % Axioms used in derivation (3): refl_axiom, trans_axiom, axiom1
% 2.95/1.70 % No. of inferences in proof: 10
% 2.95/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1164 ms resp. 685 ms w/o parsing
% 2.95/1.73 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.95/1.73 % [INFO] Killing All external provers ...
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