TSTP Solution File: LCL901+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : LCL901+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 07:57:04 EDT 2024
% Result : Theorem 3.43s 1.76s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 37 ( 20 unt; 5 typ; 0 def)
% Number of atoms : 50 ( 17 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 190 ( 2 ~; 0 |; 5 &; 170 @)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 ^ 61 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'==>\'_type',type,
'\'==>\'': $i > $i > $i ).
thf('\'1\'_type',type,
'\'1\'': $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf('\'+\'_type',type,
'\'+\'': $i > $i > $i ).
thf('\'>=\'_type',type,
'\'>=\'': $i > $i > $o ).
thf(14,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ '\'1\'' )
= '\'1\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).
thf(52,plain,
! [A: $i] :
( ( '\'+\'' @ A @ '\'1\'' )
= '\'1\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
thf(41,plain,
! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i] :
( ( '\'==>\'' @ ( '\'==>\'' @ ( '\'==>\'' @ A @ '\'1\'' ) @ A ) @ A )
= '\'0\'' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( '\'==>\'' @ ( '\'==>\'' @ ( '\'==>\'' @ A @ '\'1\'' ) @ A ) @ A )
= '\'0\'' ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i] :
( ( '\'==>\'' @ ( '\'==>\'' @ ( '\'==>\'' @ A @ '\'1\'' ) @ A ) @ A )
= '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_11) ).
thf(49,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ C ) )
=> ( '\'>=\'' @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ C ) )
=> ( '\'>=\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
thf(58,plain,
! [A: $i] :
( ( '\'+\'' @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C )
<=> ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C )
=> ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) ) )
& ( ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) )
=> ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
thf(20,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_10) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
! [A: $i] : ( '\'>=\'' @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
thf(29,plain,
! [A: $i] : ( '\'>=\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ '\'0\'' )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
thf(26,plain,
! [A: $i] :
( ( '\'+\'' @ A @ '\'0\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( '\'==>\'' @ ( '\'==>\'' @ A @ B ) @ B )
= ( '\'==>\'' @ ( '\'==>\'' @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( '\'==>\'' @ ( '\'==>\'' @ A @ B ) @ B )
= ( '\'==>\'' @ ( '\'==>\'' @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(126,plain,
$false,
inference(e,[status(thm)],[52,33,41,17,49,31,43,58,36,20,46,29,26,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LCL901+1 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.10 % Command : run_Leo-III %s %d
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon May 6 11:55:54 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.83 % [INFO] Parsing done (120ms).
% 0.96/0.84 % [INFO] Running in sequential loop mode.
% 1.28/1.05 % [INFO] eprover registered as external prover.
% 1.28/1.05 % [INFO] cvc4 registered as external prover.
% 1.28/1.06 % [INFO] Scanning for conjecture ...
% 1.47/1.11 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.55/1.14 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.65/1.16 % [INFO] Problem is first-order (TPTP FOF).
% 1.65/1.16 % [INFO] Type checking passed.
% 1.65/1.16 % [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 ...
% 3.43/1.76 % External prover 'e' found a proof!
% 3.43/1.76 % [INFO] Killing All external provers ...
% 3.43/1.76 % Time passed: 1350ms (effective reasoning time: 920ms)
% 3.43/1.76 % 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)>
% 3.43/1.76 % Axioms used in derivation (14): sos_01, sos_05, sos_02, sos_11, sos_07, sos_13, sos_12, sos_06, sos_09, sos_03, sos_04, sos_10, sos_08, sos_14
% 3.43/1.76 % No. of inferences in proof: 32
% 3.43/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1350 ms resp. 920 ms w/o parsing
% 3.43/1.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.43/1.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------