TSTP Solution File: SYO069^4.001 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SYO069^4.001 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 08:55:42 EDT 2024
% Result : Theorem 70.28s 12.87s
% Output : Refutation 70.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 22 ( 7 unt; 10 typ; 4 def)
% Number of atoms : 172 ( 4 equ; 0 cnn)
% Maximal formula atoms : 54 ( 14 avg)
% Number of connectives : 252 ( 14 ~; 12 |; 7 &; 193 @)
% ( 0 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 25 ( 25 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 36 ( 3 ^ 33 !; 0 ?; 36 :)
% 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(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(iand_def,definition,
iand = mand ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(iimplies_def,definition,
( iimplies
= ( ^ [A: $i > $o,B: $i > $o] : ( mimplies @ ( mbox_s4 @ A ) @ ( mbox_s4 @ B ) ) ) ) ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(ivalid_def,definition,
( ivalid
= ( '!' @ $i ) ) ).
thf(a0_type,type,
a0: $i > $o ).
thf(a1_type,type,
a1: $i > $o ).
thf(b0_type,type,
b0: $i > $o ).
thf(b1_type,type,
b1: $i > $o ).
thf(f_type,type,
f: $i > $o ).
thf(1,conjecture,
ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ( ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ b0 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) @ ( iatom @ f ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(5,plain,
~ ! [A: $i] :
( ( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( a0 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( f @ C ) ) )
& ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( ~ ! [D: $i] :
( ( irel @ C @ D )
=> ( b1 @ D ) )
| ! [D: $i] :
( ( irel @ C @ D )
=> ( b0 @ D ) ) ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( a1 @ C ) ) )
& ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( ~ ! [D: $i] :
( ( irel @ C @ D )
=> ( b0 @ D ) )
| ! [D: $i] :
( ( irel @ C @ D )
=> ( a1 @ D ) ) ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( a0 @ C ) ) ) ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( f @ B ) ) )
& ( ~ ! [B: $i] :
( ( irel @ A @ B )
=> ( ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( ~ ! [D: $i] :
( ( irel @ C @ D )
=> ( b0 @ D ) )
| ! [D: $i] :
( ( irel @ C @ D )
=> ( a1 @ D ) ) ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( a0 @ C ) ) )
& ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( ~ ! [D: $i] :
( ( irel @ C @ D )
=> ( b1 @ D ) )
| ! [D: $i] :
( ( irel @ C @ D )
=> ( b0 @ D ) ) ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( a1 @ C ) ) )
& ( ~ ! [C: $i] :
( ( irel @ B @ C )
=> ( a0 @ C ) )
| ! [C: $i] :
( ( irel @ B @ C )
=> ( f @ C ) ) ) ) )
| ! [B: $i] :
( ( irel @ A @ B )
=> ( f @ B ) ) ) ),
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(49,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(51,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(22830,plain,
$false,
inference(cvc4,[status(thm)],[5,49,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO069^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n028.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 08:44:39 EDT 2024
% 0.17/0.37 % CPUTime :
% 1.02/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.09 % [INFO] Parsing done (147ms).
% 1.57/1.10 % [INFO] Running in sequential loop mode.
% 1.99/1.32 % [INFO] eprover registered as external prover.
% 1.99/1.32 % [INFO] cvc4 registered as external prover.
% 1.99/1.32 % [INFO] Scanning for conjecture ...
% 2.17/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 2.17/1.44 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.17/1.44 % [INFO] Problem is higher-order (TPTP THF).
% 2.17/1.44 % [INFO] Type checking passed.
% 2.17/1.44 % [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 ...
% 70.28/12.87 % External prover 'cvc4' found a proof!
% 70.28/12.87 % [INFO] Killing All external provers ...
% 70.28/12.87 % Time passed: 12324ms (effective reasoning time: 11769ms)
% 70.28/12.87 % 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)>
% 70.28/12.87 % Axioms used in derivation (2): refl_axiom, trans_axiom
% 70.28/12.87 % No. of inferences in proof: 8
% 70.28/12.87 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 12324 ms resp. 11769 ms w/o parsing
% 70.28/12.90 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 70.28/12.90 % [INFO] Killing All external provers ...
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