%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.19
% Problem : LCL506+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n027.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 : Wed Oct 1 12:41:24 PM UTC 2025
% Result : Theorem 35.36s 6.43s
% Output : Refutation 35.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 80 ( 8 ~; 4 |; 2 &; 60 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(and_1_type,type,
and_1: $o ).
thf(kn2_type,type,
kn2: $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(sk54_type,type,
sk54: $i ).
thf(sk55_type,type,
sk55: $i ).
thf(44,axiom,
( and_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(152,plain,
( ( and_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> and_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(153,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk54 @ sk55 ) @ sk54 ) )
| and_1 ),
inference(cnf,[status(esa)],[152]) ).
thf(1,conjecture,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(2,negated_conjecture,
~ and_1,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ and_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6999,plain,
( ~ ( is_a_theorem @ ( implies @ ( and @ sk54 @ sk55 ) @ sk54 ) )
| $false ),
inference(rewrite,[status(thm)],[153,45]) ).
thf(7000,plain,
~ ( is_a_theorem @ ( implies @ ( and @ sk54 @ sk55 ) @ sk54 ) ),
inference(simp,[status(thm)],[6999]) ).
thf(18,axiom,
( kn2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(69,plain,
( ( kn2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) )
=> kn2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ kn2
| ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(5,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
thf(48,plain,
kn2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7032,plain,
! [B: $i,A: $i] :
( ~ $true
| ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ) ),
inference(rewrite,[status(thm)],[71,48]) ).
thf(7033,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( implies @ ( and @ A @ B ) @ A ) ),
inference(simp,[status(thm)],[7032]) ).
thf(7034,plain,
~ $true,
inference(rewrite,[status(thm)],[7000,7033]) ).
thf(7035,plain,
$false,
inference(simp,[status(thm)],[7034]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL506+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.03/0.12 % Command : run_Leo-III %s %d SAT
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Sep 30 13:27:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.95/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.05 % [INFO] Parsing done (136ms).
% 1.41/1.06 % [INFO] Running in sequential loop mode.
% 1.83/1.26 % [INFO] nitpick registered as external prover.
% 1.83/1.27 % [INFO] Scanning for conjecture ...
% 1.83/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 2.03/1.36 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 2.17/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.17/1.42 % [INFO] Type checking passed.
% 2.17/1.42 % [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 ...
% 35.36/6.43 % [INFO] Killing All external provers ...
% 35.36/6.43 % Time passed: 5920ms (effective reasoning time: 5370ms)
% 35.36/6.43 % 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)>
% 35.36/6.43 % Axioms used in derivation (3): and_1, kn2, rosser_kn2
% 35.36/6.43 % No. of inferences in proof: 17
% 35.36/6.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5920 ms resp. 5370 ms w/o parsing
% 35.36/6.45 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 35.36/6.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------