TSTP Solution File: SWV048+1 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SWV048+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 05:50:23 EDT 2024
% Result : Theorem 166.14s 29.78s
% Output : Refutation 166.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 62 ( 29 unt; 21 typ; 0 def)
% Number of atoms : 87 ( 53 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 405 ( 35 ~; 19 |; 18 &; 324 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 15 con; 0-3 aty)
% Number of variables : 15 ( 0 ^ 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
thf(pv78_type,type,
pv78: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(minus_type,type,
minus: $i > $i > $i ).
thf(n135300_type,type,
n135300: $i ).
thf(n1_type,type,
n1: $i ).
thf(a_select3_type,type,
a_select3: $i > $i > $i > $i ).
thf(q_type,type,
q: $i ).
thf(pv79_type,type,
pv79: $i ).
thf(pv35_type,type,
pv35: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(n5_type,type,
n5: $i ).
thf(times_type,type,
times: $i > $i > $i ).
thf(pv81_type,type,
pv81: $i ).
thf(a_select2_type,type,
a_select2: $i > $i > $i ).
thf(x_type,type,
x: $i ).
thf(true_type,type,
true: $o ).
thf(succ_type,type,
succ: $i > $i ).
thf(pred_type,type,
pred: $i > $i ).
thf(tptp_minus_1_type,type,
tptp_minus_1: $i ).
thf(sk1_type,type,
sk1: $o ).
thf(31,axiom,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
thf(173,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(174,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
= n0 ),
inference(lifteq,[status(thm)],[174]) ).
thf(1,conjecture,
( ( ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
=> ( ( ( n0 != pv78 )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
& ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv78 )
=> true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0016) ).
thf(2,negated_conjecture,
~ ( ( ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
=> ( ( ( n0 != pv78 )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
& ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv78 )
=> true ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(93,plain,
~ ( ( ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) )
=> ( ( ( n0 != pv78 )
=> ( ( n0
= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
& ( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
& ( leq @ n0 @ pv35 )
& ( leq @ pv35 @ ( minus @ n5 @ n1 ) ) ) )
& ( ( n0 = pv78 )
=> true ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(98,plain,
( ( n0
!= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) )
| ( pv78
!= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) )
| ~ ( leq @ n0 @ pv35 )
| ~ ( leq @ pv35 @ ( minus @ n5 @ n1 ) )
| ~ sk1 ),
inference(cnf,[status(esa)],[93]) ).
thf(102,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
!= n0 )
| ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
!= pv78 )
| ~ ( leq @ n0 @ pv35 )
| ~ ( leq @ pv35 @ ( minus @ n5 @ n1 ) )
| ~ sk1 ),
inference(lifteq,[status(thm)],[98]) ).
thf(100,plain,
leq @ n0 @ pv35,
inference(cnf,[status(esa)],[93]) ).
thf(96,plain,
( sk1
| ~ true ),
inference(cnf,[status(esa)],[93]) ).
thf(44,axiom,
true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ttrue) ).
thf(321,plain,
true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(565,plain,
( sk1
| ~ $true ),
inference(rewrite,[status(thm)],[96,321]) ).
thf(566,plain,
sk1,
inference(simp,[status(thm)],[565]) ).
thf(95,plain,
leq @ pv35 @ ( minus @ n5 @ n1 ),
inference(cnf,[status(esa)],[93]) ).
thf(572,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
!= n0 )
| ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
!= pv78 )
| ~ $true
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[102,100,566,95]) ).
thf(573,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
!= n0 )
| ( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
!= pv78 ) ),
inference(simp,[status(thm)],[572]) ).
thf(94,plain,
( pv78
= ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(104,plain,
( ( sum @ n0 @ ( minus @ n135300 @ n1 ) @ ( a_select3 @ q @ pv79 @ pv35 ) )
= pv78 ),
inference(lifteq,[status(thm)],[94]) ).
thf(698,plain,
( ( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
!= n0 )
| ( pv78 != pv78 ) ),
inference(rewrite,[status(thm)],[573,104]) ).
thf(699,plain,
( ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) )
!= n0 ),
inference(simp,[status(thm)],[698]) ).
thf(8209,plain,
! [A: $i] :
( ( sum @ n0 @ tptp_minus_1 @ A )
!= ( sum @ n0 @ ( minus @ n0 @ n1 ) @ ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) ),
inference(paramod_ordered,[status(thm)],[175,699]) ).
thf(8237,plain,
! [A: $i] :
( ( n0 != n0 )
| ( ( minus @ n0 @ n1 )
!= tptp_minus_1 )
| ( A
!= ( times @ ( a_select3 @ q @ pv81 @ pv35 ) @ ( a_select2 @ x @ pv81 ) ) ) ),
inference(simp,[status(thm)],[8209]) ).
thf(8268,plain,
( ( minus @ n0 @ n1 )
!= tptp_minus_1 ),
inference(simp,[status(thm)],[8237]) ).
thf(39,axiom,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
thf(222,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(223,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(cnf,[status(esa)],[222]) ).
thf(224,plain,
! [A: $i] :
( ( minus @ A @ n1 )
= ( pred @ A ) ),
inference(lifteq,[status(thm)],[223]) ).
thf(23513,plain,
( ( pred @ n0 )
!= tptp_minus_1 ),
inference(rewrite,[status(thm)],[8268,224]) ).
thf(49,axiom,
( ( succ @ tptp_minus_1 )
= n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
thf(330,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(331,plain,
( ( succ @ tptp_minus_1 )
= n0 ),
inference(lifteq,[status(thm)],[330]) ).
thf(14,axiom,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
thf(127,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(128,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(cnf,[status(esa)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( pred @ ( succ @ A ) )
= A ),
inference(lifteq,[status(thm)],[128]) ).
thf(3754,plain,
! [A: $i] :
( ( ( pred @ n0 )
= A )
| ( ( succ @ tptp_minus_1 )
!= ( succ @ A ) ) ),
inference(paramod_ordered,[status(thm)],[331,129]) ).
thf(3755,plain,
( ( pred @ n0 )
= tptp_minus_1 ),
inference(pattern_uni,[status(thm)],[3754:[bind(A,$thf( tptp_minus_1 ))]]) ).
thf(23527,plain,
tptp_minus_1 != tptp_minus_1,
inference(rewrite,[status(thm)],[23513,3755]) ).
thf(23528,plain,
$false,
inference(simp,[status(thm)],[23527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV048+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 09:03:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 1.17/1.09 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.35 % [INFO] Parsing done (254ms).
% 1.78/1.36 % [INFO] Running in sequential loop mode.
% 2.54/1.80 % [INFO] nitpick registered as external prover.
% 2.54/1.81 % [INFO] Scanning for conjecture ...
% 2.82/1.95 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 3.16/2.07 % [INFO] Axiom selection finished. Selected 90 axioms (removed 1 axioms).
% 3.61/2.22 % [INFO] Problem is first-order (TPTP FOF).
% 3.61/2.25 % [INFO] Type checking passed.
% 3.61/2.25 % [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 ...
% 166.14/29.77 % [INFO] Killing All external provers ...
% 166.14/29.77 % Time passed: 29255ms (effective reasoning time: 28403ms)
% 166.14/29.77 % 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)>
% 166.14/29.78 % Axioms used in derivation (5): pred_minus_1, ttrue, succ_tptp_minus_1, sum_plus_base, pred_succ
% 166.14/29.78 % No. of inferences in proof: 41
% 166.14/29.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 29255 ms resp. 28403 ms w/o parsing
% 166.14/29.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 166.14/29.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------