TSTP Solution File: LCL894+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL894+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n019.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 : Fri May 19 11:32:28 EDT 2023
% Result : Theorem 5.41s 2.29s
% Output : Refutation 5.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 35 ( 13 unt; 7 typ; 0 def)
% Number of atoms : 55 ( 10 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 213 ( 2 ~; 0 |; 10 &; 184 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf('\'>=\'_type',type,
'\'>=\'': $i > $i > $o ).
thf(c_type,type,
c: $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf('\'+\'_type',type,
'\'+\'': $i > $i > $i ).
thf('\'==>\'_type',type,
'\'==>\'': $i > $i > $i ).
thf('\'0\'_type',type,
'\'0\'': $i ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_01) ).
thf(21,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'+\'' @ ( '\'+\'' @ A @ B ) @ C )
= ( '\'+\'' @ A @ ( '\'+\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ ( '\'==>\'' @ A @ B ) )
= ( '\'+\'' @ B @ ( '\'==>\'' @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ ( '\'==>\'' @ A @ B ) )
= ( '\'+\'' @ B @ ( '\'==>\'' @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ C @ A ) @ ( '\'==>\'' @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i] : ( '\'>=\'' @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
thf(30,plain,
! [A: $i] : ( '\'>=\'' @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
thf(42,plain,
! [A: $i] : ( '\'>=\'' @ A @ '\'0\'' ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( '\'+\'' @ A @ B )
= ( '\'+\'' @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ ( '\'+\'' @ A @ B ) @ C )
<=> ( '\'>=\'' @ B @ ( '\'==>\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
thf(37,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(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ C ) )
=> ( '\'>=\'' @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_05) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ C ) )
=> ( '\'>=\'' @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( '\'>=\'' @ A @ B )
& ( '\'>=\'' @ B @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'+\'' @ A @ C ) @ ( '\'+\'' @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i] :
( ( '\'+\'' @ A @ '\'0\'' )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
thf(27,plain,
! [A: $i] :
( ( '\'+\'' @ A @ '\'0\'' )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
thf(47,plain,
! [A: $i,B: $i,C: $i] :
( ( '\'>=\'' @ A @ B )
=> ( '\'>=\'' @ ( '\'==>\'' @ B @ C ) @ ( '\'==>\'' @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,conjecture,
( ( ( '\'>=\'' @ c @ a )
& ( '\'>=\'' @ c @ b ) )
<=> ( '\'>=\'' @ c @ ( '\'+\'' @ a @ ( '\'==>\'' @ a @ b ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_13) ).
thf(2,negated_conjecture,
~ ( ( ( '\'>=\'' @ c @ a )
& ( '\'>=\'' @ c @ b ) )
<=> ( '\'>=\'' @ c @ ( '\'+\'' @ a @ ( '\'==>\'' @ a @ b ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ( ( ( ( '\'>=\'' @ c @ a )
& ( '\'>=\'' @ c @ b ) )
=> ( '\'>=\'' @ c @ ( '\'+\'' @ a @ ( '\'==>\'' @ a @ b ) ) ) )
& ( ( '\'>=\'' @ c @ ( '\'+\'' @ a @ ( '\'==>\'' @ a @ b ) ) )
=> ( ( '\'>=\'' @ c @ a )
& ( '\'>=\'' @ c @ b ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(279,plain,
$false,
inference(e,[status(thm)],[21,53,50,30,42,24,37,32,34,44,27,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL894+1 : TPTP v8.1.2. Released v5.5.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 16:19:43 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.98 % [INFO] Parsing done (122ms).
% 1.27/0.98 % [INFO] Running in sequential loop mode.
% 1.71/1.24 % [INFO] eprover registered as external prover.
% 1.71/1.24 % [INFO] cvc4 registered as external prover.
% 1.71/1.24 % [INFO] Scanning for conjecture ...
% 1.80/1.30 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.80/1.33 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.00/1.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.37 % [INFO] Type checking passed.
% 2.14/1.37 % [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 ...
% 5.41/2.28 % External prover 'e' found a proof!
% 5.41/2.28 % [INFO] Killing All external provers ...
% 5.41/2.28 % Time passed: 1769ms (effective reasoning time: 1296ms)
% 5.41/2.28 % 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)>
% 5.41/2.29 % Axioms used in derivation (12): sos_01, sos_05, sos_02, sos_11, sos_07, sos_08, sos_12, sos_06, sos_09, sos_03, sos_04, sos_10
% 5.41/2.29 % No. of inferences in proof: 28
% 5.41/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1769 ms resp. 1296 ms w/o parsing
% 5.41/2.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.41/2.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------