TSTP Solution File: SYN333+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYN333+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 08:18:04 EDT 2024
% Result : Theorem 2.33s 1.61s
% Output : Refutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 19 ( 3 unt; 6 typ; 0 def)
% Number of atoms : 52 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 186 ( 21 ~; 15 |; 16 &; 126 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 0 ^ 23 !; 8 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_f_type,type,
big_f: $i > $i > $o ).
thf(big_g_type,type,
big_g: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i ).
thf(sk3_type,type,
sk3: $i > $i > $i ).
thf(sk4_type,type,
sk4: $i > $i > $i ).
thf(1,conjecture,
? [A: $i,B: $i] :
! [C: $i] :
( ( big_f @ A @ B )
=> ( ( big_f @ B @ C )
& ( big_f @ C @ C )
& ( ( ( big_f @ A @ B )
& ( big_g @ A @ B ) )
=> ( ( big_g @ A @ C )
& ( big_g @ C @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_14_5) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
! [C: $i] :
( ( big_f @ A @ B )
=> ( ( big_f @ B @ C )
& ( big_f @ C @ C )
& ( ( ( big_f @ A @ B )
& ( big_g @ A @ B ) )
=> ( ( big_g @ A @ C )
& ( big_g @ C @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ? [A: $i,B: $i] :
! [C: $i] :
( ( big_f @ A @ B )
=> ( ( big_f @ B @ C )
& ( big_f @ C @ C )
& ( ( ( big_f @ A @ B )
& ( big_g @ A @ B ) )
=> ( ( big_g @ A @ C )
& ( big_g @ C @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] : ( big_f @ A @ B )
=> ? [A: $i,B: $i] :
( ! [C: $i] : ( big_f @ B @ C )
& ! [C: $i] : ( big_f @ C @ C )
& ( ( ( big_f @ A @ B )
& ( big_g @ A @ B ) )
=> ( ! [C: $i] : ( big_g @ A @ C )
& ! [C: $i] : ( big_g @ C @ C ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
| ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
| ~ ( big_g @ A @ ( sk3 @ B @ A ) )
| ~ ( big_g @ ( sk4 @ B @ A ) @ ( sk4 @ B @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
| ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
| ~ ( big_g @ A @ ( sk3 @ B @ A ) )
| ~ ( big_g @ ( sk4 @ B @ A ) @ ( sk4 @ B @ A ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(8,plain,
! [B: $i,A: $i] : ( big_f @ A @ B ),
inference(cnf,[status(esa)],[4]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
| ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
| ( big_g @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( big_f @ B @ ( sk1 @ B @ A ) )
| ~ ( big_f @ ( sk2 @ B @ A ) @ ( sk2 @ B @ A ) )
| ( big_g @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(12,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ $true
| ( big_g @ A @ B ) ),
inference(rewrite,[status(thm)],[10,8]) ).
thf(13,plain,
! [B: $i,A: $i] : ( big_g @ A @ B ),
inference(simp,[status(thm)],[12]) ).
thf(16,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[9,8,13]) ).
thf(17,plain,
$false,
inference(simp,[status(thm)],[16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN333+1 : TPTP v8.2.0. Released v2.0.0.
% 0.07/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 14:23:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.81/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.93/0.90 % [INFO] Parsing done (108ms).
% 0.93/0.91 % [INFO] Running in sequential loop mode.
% 1.47/1.15 % [INFO] nitpick registered as external prover.
% 1.47/1.16 % [INFO] Scanning for conjecture ...
% 1.56/1.23 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.70/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.76/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.76/1.26 % [INFO] Type checking passed.
% 1.76/1.27 % [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 ...
% 2.33/1.60 % [INFO] Killing All external provers ...
% 2.33/1.61 % Time passed: 1149ms (effective reasoning time: 693ms)
% 2.33/1.61 % 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)>
% 2.33/1.61 % Axioms used in derivation (0):
% 2.33/1.61 % No. of inferences in proof: 13
% 2.33/1.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1149 ms resp. 693 ms w/o parsing
% 2.48/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.48/1.66 % [INFO] Killing All external provers ...
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