%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.19
% Problem : LCL484+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n029.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 12:41:23 PM UTC 2025
% Result : Theorem 49.66s 8.20s
% Output : Refutation 49.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 337 ( 22 ~; 14 |; 2 &; 287 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(implies_1_type,type,
implies_1: $o ).
thf(op_implies_or_type,type,
op_implies_or: $o ).
thf(op_implies_and_type,type,
op_implies_and: $o ).
thf(op_or_type,type,
op_or: $o ).
thf(and_type,type,
and: $i > $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(r2_type,type,
r2: $o ).
thf(is_a_theorem_type,type,
is_a_theorem: $i > $o ).
thf(sk54_type,type,
sk54: $i ).
thf(sk55_type,type,
sk55: $i ).
thf(46,axiom,
( implies_1
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(156,plain,
( ( implies_1
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ A @ ( implies @ B @ A ) ) )
=> implies_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(157,plain,
( ~ ( is_a_theorem @ ( implies @ sk54 @ ( implies @ sk55 @ sk54 ) ) )
| implies_1 ),
inference(cnf,[status(esa)],[156]) ).
thf(1,conjecture,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(2,negated_conjecture,
~ implies_1,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(47,plain,
~ implies_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(618,plain,
( ~ ( is_a_theorem @ ( implies @ sk54 @ ( implies @ sk55 @ sk54 ) ) )
| $false ),
inference(rewrite,[status(thm)],[157,47]) ).
thf(619,plain,
~ ( is_a_theorem @ ( implies @ sk54 @ ( implies @ sk55 @ sk54 ) ) ),
inference(simp,[status(thm)],[618]) ).
thf(16,axiom,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(65,plain,
( op_implies_or
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ op_implies_or
| ( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( or @ ( not @ A ) @ B )
= ( implies @ A @ B ) )
| ~ op_implies_or ),
inference(lifteq,[status(thm)],[66]) ).
thf(3,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
thf(48,plain,
op_implies_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(61,plain,
( op_or
=> ! [A: $i,B: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ op_or
| ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ op_or ),
inference(lifteq,[status(thm)],[62]) ).
thf(8,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(53,plain,
op_or,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[63,53]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( or @ A @ B )
= ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(675,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[67,48,332]) ).
thf(676,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[675]) ).
thf(677,plain,
~ ( is_a_theorem @ ( not @ ( and @ ( not @ ( not @ sk54 ) ) @ ( not @ ( implies @ sk55 @ sk54 ) ) ) ) ),
inference(rewrite,[status(thm)],[619,676]) ).
thf(697,plain,
~ ( is_a_theorem @ ( not @ ( and @ ( not @ ( not @ sk54 ) ) @ ( not @ ( not @ ( and @ ( not @ ( not @ sk55 ) ) @ ( not @ sk54 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[677,676]) ).
thf(20,axiom,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(73,plain,
( op_implies_and
=> ! [A: $i,B: $i] :
( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ op_implies_and
| ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ op_implies_and ),
inference(lifteq,[status(thm)],[74]) ).
thf(5,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(50,plain,
op_implies_and,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2904,plain,
! [B: $i,A: $i] :
( ( ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ B ) ) )
= ( not @ ( and @ A @ ( not @ B ) ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[75,50,676]) ).
thf(2905,plain,
! [B: $i,A: $i] :
( ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ B ) ) )
= ( not @ ( and @ A @ ( not @ B ) ) ) ),
inference(simp,[status(thm)],[2904]) ).
thf(2918,plain,
~ ( is_a_theorem @ ( not @ ( and @ sk54 @ ( not @ ( not @ ( and @ ( not @ ( not @ sk55 ) ) @ ( not @ sk54 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[697,2905]) ).
thf(2963,plain,
~ ( is_a_theorem @ ( not @ ( and @ sk54 @ ( not @ ( not @ ( and @ sk55 @ ( not @ sk54 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2918,2905]) ).
thf(25,axiom,
( r2
<=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(88,plain,
( ( r2
=> ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) )
& ( ! [A: $i,B: $i] : ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) )
=> r2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ r2
| ( is_a_theorem @ ( implies @ B @ ( or @ A @ B ) ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(18,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
thf(71,plain,
r2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2798,plain,
! [B: $i,A: $i] :
( ~ $true
| ( is_a_theorem @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( or @ A @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[90,676,71]) ).
thf(2799,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( not @ ( and @ ( not @ ( not @ B ) ) @ ( not @ ( or @ A @ B ) ) ) ) ),
inference(simp,[status(thm)],[2798]) ).
thf(2908,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( not @ ( and @ B @ ( not @ ( or @ A @ B ) ) ) ) ),
inference(rewrite,[status(thm)],[2799,2905]) ).
thf(3166,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( not @ ( and @ B @ ( not @ ( not @ ( and @ ( not @ A ) @ ( not @ B ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[2908,332]) ).
thf(3205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( is_a_theorem @ ( not @ ( and @ D @ ( not @ ( not @ ( and @ A @ ( not @ B ) ) ) ) ) ) )
| ( ( not @ ( and @ ( not @ ( not @ A ) ) @ ( not @ B ) ) )
!= ( not @ ( and @ ( not @ C ) @ ( not @ D ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2905,3166]) ).
thf(3206,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( not @ ( and @ A @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[3205:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(3217,plain,
! [B: $i,A: $i] : ( is_a_theorem @ ( not @ ( and @ A @ ( not @ ( not @ ( and @ B @ ( not @ A ) ) ) ) ) ) ),
inference(simp,[status(thm)],[3206]) ).
thf(3311,plain,
~ $true,
inference(rewrite,[status(thm)],[2963,3217]) ).
thf(3312,plain,
$false,
inference(simp,[status(thm)],[3311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL484+1 : TPTP v9.2.0. Bugfixed v9.2.0.
% 0.11/0.12 % Command : run_Leo-III %s %d SAT
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Sep 30 14:26:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.85/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/0.99 % [INFO] Parsing done (128ms).
% 1.16/1.00 % [INFO] Running in sequential loop mode.
% 1.81/1.21 % [INFO] nitpick registered as external prover.
% 1.81/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 44 axioms. Running axiom selection ...
% 1.91/1.31 % [INFO] Axiom selection finished. Selected 44 axioms (removed 0 axioms).
% 2.18/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 2.18/1.37 % [INFO] Type checking passed.
% 2.18/1.37 % [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 ...
% 49.66/8.20 % [INFO] Killing All external provers ...
% 49.66/8.20 % Time passed: 7683ms (effective reasoning time: 7197ms)
% 49.66/8.20 % 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)>
% 49.66/8.20 % Axioms used in derivation (9): principia_r2, hilbert_op_implies_and, hilbert_op_or, op_implies_and, r2, implies_1, principia_op_implies_or, op_or, op_implies_or
% 49.66/8.20 % No. of inferences in proof: 50
% 49.66/8.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7683 ms resp. 7197 ms w/o parsing
% 49.66/8.23 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.66/8.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------