TSTP Solution File: SWW486_5 by Leo-III-SAT---1.7.15
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.15
% Problem : SWW486_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d SAT
% Computer : n023.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 : Mon Jun 24 18:25:28 EDT 2024
% Result : Theorem 90.01s 13.55s
% Output : Refutation 90.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 496 ( 15 ~; 6 |; 0 &; 473 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 19 ( 0 ^ 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(real_type,type,
real: $tType ).
thf(comm_semiring_0_type,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(pCons_type,type,
pCons:
!>[TA: $tType] : ( TA > ( poly1 @ TA ) > ( poly1 @ TA ) ) ).
thf(poly_type,type,
poly:
!>[TA: $tType] : ( ( poly1 @ TA ) > ( fun @ TA @ TA ) ) ).
thf(norm_norm_type,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(c_type,type,
c: complex ).
thf(cs_type,type,
cs: poly1 @ complex ).
thf(z_type,type,
z: complex ).
thf(53,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
= ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_poly__pCons) ).
thf(298,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA,B: poly1 @ TA,C: TA] :
( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
= ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(299,plain,
! [TA: $tType,C: TA,B: poly1 @ TA,A: TA] :
( ~ ( comm_semiring_0 @ TA )
| ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
= ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) ) ),
inference(cnf,[status(esa)],[298]) ).
thf(300,plain,
! [TA: $tType,C: TA,B: poly1 @ TA,A: TA] :
( ( ( aa @ TA @ TA @ ( poly @ TA @ ( pCons @ TA @ C @ B ) ) @ A )
= ( plus_plus @ TA @ C @ ( times_times @ TA @ A @ ( aa @ TA @ TA @ ( poly @ TA @ B ) @ A ) ) ) )
| ~ ( comm_semiring_0 @ TA ) ),
inference(lifteq,[status(thm)],[299]) ).
thf(48,axiom,
ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096) ).
thf(285,plain,
ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(1,conjecture,
ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(187,plain,
~ ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4661,plain,
( ( ord_less_eq @ real @ ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
!= ( ord_less_eq @ real @ ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) @ ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[285,187]) ).
thf(4746,plain,
( ( ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) )
!= ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
| ( ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) )
!= ( plus_plus @ real @ ( norm_norm @ complex @ c ) @ ( norm_norm @ complex @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
inference(simp,[status(thm)],[4661]) ).
thf(4753,plain,
( ( norm_norm @ complex @ ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) )
!= ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ),
inference(simp,[status(thm)],[4746]) ).
thf(9630,plain,
! [C: complex,B: poly1 @ complex,A: complex] :
( ~ ( comm_semiring_0 @ complex )
| ( ( norm_norm @ complex @ ( plus_plus @ complex @ C @ ( times_times @ complex @ A @ ( aa @ complex @ complex @ ( poly @ complex @ B ) @ A ) ) ) )
!= ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) )
| ( ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ C @ B ) ) @ A )
!= ( aa @ complex @ complex @ ( poly @ complex @ ( pCons @ complex @ c @ cs ) ) @ z ) ) ),
inference(paramod_ordered,[status(thm)],[300,4753]) ).
thf(9631,plain,
( ~ ( comm_semiring_0 @ complex )
| ( ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) )
!= ( norm_norm @ complex @ ( plus_plus @ complex @ c @ ( times_times @ complex @ z @ ( aa @ complex @ complex @ ( poly @ complex @ cs ) @ z ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[9630:[bind(A,$thf( z )),bind(B,$thf( cs )),bind(C,$thf( c ))]]) ).
thf(9723,plain,
~ ( comm_semiring_0 @ complex ),
inference(simp,[status(thm)],[9631]) ).
thf(182,axiom,
comm_semiring_0 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__0) ).
thf(618,plain,
comm_semiring_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(9851,plain,
~ $true,
inference(rewrite,[status(thm)],[9723,618]) ).
thf(9852,plain,
$false,
inference(simp,[status(thm)],[9851]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWW486_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.13 % Command : run_Leo-III %s %d SAT
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jun 19 06:14:10 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.82/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/0.99 % [INFO] Parsing done (162ms).
% 1.38/1.00 % [INFO] Running in sequential loop mode.
% 1.88/1.21 % [INFO] nitpick registered as external prover.
% 1.88/1.22 % [INFO] Scanning for conjecture ...
% 2.16/1.31 % [INFO] Found a conjecture (or negated_conjecture) and 186 axioms. Running axiom selection ...
% 2.44/1.38 % [INFO] Axiom selection finished. Selected 184 axioms (removed 2 axioms).
% 2.77/1.50 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.77/1.51 % [INFO] Type checking passed.
% 2.77/1.52 % [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 ...
% 90.01/13.55 % [INFO] Killing All external provers ...
% 90.01/13.55 % Time passed: 13042ms (effective reasoning time: 12544ms)
% 90.01/13.55 % 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)>
% 90.01/13.55 % Axioms used in derivation (3): fact_4_poly__pCons, fact_0__096cmod_A_Ic_A_L_Az_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096, arity_Complex_Ocomplex___Rings_Ocomm__semiring__0
% 90.01/13.55 % No. of inferences in proof: 19
% 90.01/13.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13042 ms resp. 12544 ms w/o parsing
% 90.01/13.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 90.01/13.59 % [INFO] Killing All external provers ...
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