TSTP Solution File: SYN078+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SYN078+1 : TPTP v8.2.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.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 08:17:26 EDT 2024
% Result : Theorem 2.93s 1.98s
% Output : Refutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 6 unt; 6 typ; 0 def)
% Number of atoms : 79 ( 13 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 139 ( 28 ~; 28 |; 5 &; 66 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 0 ^ 17 !; 4 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
thf(big_p_type,type,
big_p: $i > $o ).
thf(f_type,type,
f: $i > $i ).
thf(sk1_type,type,
sk1: $o ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(1,conjecture,
( ! [A: $i] :
( ? [B: $i] :
( ( big_p @ B )
& ( A
= ( f @ B ) ) )
=> ( big_p @ A ) )
<=> ! [A: $i] :
( ( big_p @ A )
=> ( big_p @ ( f @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ? [B: $i] :
( ( big_p @ B )
& ( A
= ( f @ B ) ) )
=> ( big_p @ A ) )
<=> ! [A: $i] :
( ( big_p @ A )
=> ( big_p @ ( f @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: $i] :
( ? [B: $i] :
( ( big_p @ B )
& ( A
= ( f @ B ) ) )
=> ( big_p @ A ) )
=> ! [A: $i] :
( ( big_p @ A )
=> ( big_p @ ( f @ A ) ) ) )
& ( ! [A: $i] :
( ( big_p @ A )
=> ( big_p @ ( f @ A ) ) )
=> ! [A: $i] :
( ? [B: $i] :
( ( big_p @ B )
& ( A
= ( f @ B ) ) )
=> ( big_p @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,plain,
( sk1
| ~ ( big_p @ sk3 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(10,plain,
( ( big_p @ sk2 )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ~ ( big_p @ B )
| ( A
!= ( f @ B ) )
| ( big_p @ A )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( A
!= ( f @ B ) )
| ~ ( big_p @ B )
| ( big_p @ A )
| ~ sk1 ),
inference(lifteq,[status(thm)],[9]) ).
thf(12,plain,
! [A: $i] :
( ~ ( big_p @ A )
| ( big_p @ ( f @ A ) )
| ~ sk1 ),
inference(simp,[status(thm)],[11]) ).
thf(5,plain,
( ~ ( big_p @ ( f @ sk2 ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[3]) ).
thf(23,plain,
! [A: $i] :
( ~ ( big_p @ A )
| ~ sk1
| ( ( big_p @ ( f @ A ) )
!= ( big_p @ ( f @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,5]) ).
thf(24,plain,
( ~ ( big_p @ sk2 )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk2 ))]]) ).
thf(35,plain,
( ~ sk1
| ( ( big_p @ sk2 )
!= ( big_p @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[10,24]) ).
thf(36,plain,
~ sk1,
inference(pattern_uni,[status(thm)],[35:[]]) ).
thf(64,plain,
( $false
| ~ ( big_p @ sk3 ) ),
inference(rewrite,[status(thm)],[7,36]) ).
thf(65,plain,
~ ( big_p @ sk3 ),
inference(simp,[status(thm)],[64]) ).
thf(6,plain,
( sk1
| ( big_p @ sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
! [A: $i] :
( sk1
| ~ ( big_p @ A )
| ( big_p @ ( f @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [A: $i] :
( sk1
| ~ ( big_p @ A )
| ( big_p @ ( f @ A ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(47,plain,
! [A: $i] :
( sk1
| ( big_p @ ( f @ A ) )
| ( ( big_p @ sk4 )
!= ( big_p @ A ) ) ),
inference(paramod_ordered,[status(thm)],[6,13]) ).
thf(48,plain,
( sk1
| ( big_p @ ( f @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( sk4 ))]]) ).
thf(4,plain,
( sk1
| ( sk3
= ( f @ sk4 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
( ( ( f @ sk4 )
= sk3 )
| sk1 ),
inference(lifteq,[status(thm)],[4]) ).
thf(58,plain,
( ( ( f @ sk4 )
= sk3 )
| $false ),
inference(rewrite,[status(thm)],[14,36]) ).
thf(59,plain,
( ( f @ sk4 )
= sk3 ),
inference(simp,[status(thm)],[58]) ).
thf(72,plain,
( $false
| ( big_p @ sk3 ) ),
inference(rewrite,[status(thm)],[48,36,59]) ).
thf(73,plain,
big_p @ sk3,
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
~ $true,
inference(rewrite,[status(thm)],[65,73]) ).
thf(75,plain,
$false,
inference(simp,[status(thm)],[74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SYN078+1 : TPTP v8.2.0. Released v2.0.0.
% 0.05/0.12 % Command : run_Leo-III %s %d
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % 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 : Mon May 20 13:44:09 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.76/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.00/0.88 % [INFO] Parsing done (114ms).
% 1.00/0.89 % [INFO] Running in sequential loop mode.
% 1.53/1.24 % [INFO] nitpick registered as external prover.
% 1.53/1.25 % [INFO] Scanning for conjecture ...
% 1.58/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.76/1.33 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.76/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 1.76/1.34 % [INFO] Type checking passed.
% 1.76/1.34 % [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 ...
% 2.93/1.98 % [INFO] Killing All external provers ...
% 2.93/1.98 % Time passed: 1548ms (effective reasoning time: 1083ms)
% 2.93/1.98 % 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)>
% 2.93/1.98 % Axioms used in derivation (0):
% 2.93/1.98 % No. of inferences in proof: 28
% 2.93/1.98 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1548 ms resp. 1083 ms w/o parsing
% 3.07/2.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.07/2.02 % [INFO] Killing All external provers ...
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